Representations of J₁

Permutation Representations

Points	ID	Prim	Trans	Rank	Suborbits	Char	Stab	Files
266		Primitive	1	5	1, 11, 12, 110, 132	1+56ab+76a+77a	L2(11)	m b g M	view
1045		Primitive	1	11	1, 8, 28, 563, 1685	1+56ab+76a+77bc+120abc+133a+209	23:7:3	m b g M	view
1463		Primitive	1	22	1, 12, 152, 202, 609, 1207	1+56ab+76aa+77aa+120abc+133aa+209aa	A5 × 2	m b g M	view
1540		Primitive	1	21	1, 19, 384, 576, 1149		19:6	m b g M	view
1596		Primitive	1	19	1, 11, 222, 552, 11013		11:10	m b g M	view
2926		Primitive	1	67	1, 155, 3027, 6034		D10 × D6	m b g M	view
4180		Primitive	1	107	1, 7, 144, 216, 4295		7:6	m b g M	view

Matrix Representations

Char	Ring	Dim	ID	Ind	Character	Char Rng	H1	H2	Schur	Irr	Files
0	Z	76	a	+	χ4	Z			1	Abs irr	m b g M	view
0	Z	76	b	+	χ5	Z			1	Abs irr	m b g M	view
0	Z	77	a	+	χ6	Z			1	Abs irr	m b g M	view
0	Z	112			χ2 + χ3	Z				Irr not abs irr	m b g M	view
0	Z	133	a	+	χ12	Z			1	Abs irr	m b g M	view
0	Z	154	a		χ7 + χ8	Z				Irr not abs irr	m b g M	view
0	Z	209		+	χ15	Z			1	Abs irr	m b g M	view
0	Z	266			χ13 + χ14	Z				Irr not abs irr	m b g M	view
0	Z	360			χ9 + χ10 + χ11	Z				Irr not abs irr	m b g M	view
Char	Ring	Dim	ID	Ind	Character	Char Rng	H1	H2	Schur	Irr	Files
2	GF(2)	20		+			0	0		Abs irr	m b g M	view
2	GF(4)	56	a	−			1	1		Abs irr	m b g M	view
2	GF(4)	56	b	−			1	1		Abs irr	m b g M	view
2	GF(4)	56	c	+			0	0		Abs irr	m b g M	view
2	GF(4)	56	d	+			0	0		Abs irr	m b g M	view
2	GF(2)	76	a	−			1	1		Abs irr	m b g M	view
2	GF(2)	76	b	+			0	0		Abs irr	m b g M	view
2	GF(2)	112	a				2	2		Irr not abs irr	m b g M	view
2	GF(2)	112	b				0	0		Irr not abs irr	m b g M	view
2	GF(8)	120	a	+			0	0		Abs irr	m b g M	view
2	GF(8)	120	b	+			0	0		Abs irr	m b g M	view
2	GF(8)	120	c	+			0	0		Abs irr	m b g M	view
2	GF(2)	360					0	0		Irr not abs irr	m b g M	view
Char	Ring	Dim	ID	Ind	Character	Char Rng	H1	H2	Schur	Irr	Files
3	GF(9)	56	a	+			0	0		Abs irr	m b g M	view
3	GF(9)	56	b	+			0	0		Abs irr	m b g M	view
3	GF(3)	76	a	+			1	1		Abs irr	m b g M	view
3	GF(3)	76	b	+			0	0		Abs irr	m b g M	view
3	GF(9)	77	a	+			0	0		Abs irr	m b g M	view
3	GF(9)	77	b	+			0	0		Abs irr	m b g M	view
3	GF(3)	112					0	0		Irr not abs irr	m b g M	view
3	GF(27)	120	a	+			0	0		Abs irr	m b g M	view
3	GF(27)	120	b	+			0	0		Abs irr	m b g M	view
3	GF(27)	120	c	+			0	0		Abs irr	m b g M	view
3	GF(3)	133		+			0	0		Abs irr	m b g M	view
3	GF(3)	154					0	0		Irr not abs irr	m b g M	view
3	GF(3)	360					0	0		Irr not abs irr	m b g M	view
Char	Ring	Dim	ID	Ind	Character	Char Rng	H1	H2	Schur	Irr	Files
5	GF(5)	56		+			0	0		Abs irr	m b g M	view
5	GF(5)	76	a	+			0	0		Abs irr	m b g M	view
5	GF(5)	76	b	+			1	1		Abs irr	m b g M	view
5	GF(5)	77		+			0	0		Abs irr	m b g M	view
5	GF(125)	120	a	+			0	0		Abs irr	m b g M	view
5	GF(125)	120	b	+			0	0		Abs irr	m b g M	view
5	GF(125)	120	c	+			0	0		Abs irr	m b g M	view
5	GF(5)	133		+			0	0		Abs irr	m b g M	view
5	GF(5)	360					0	0		Irr not abs irr	m b g M	view
Char	Ring	Dim	ID	Ind	Character	Char Rng	H1	H2	Schur	Irr	Files
7	GF(7)	31		+			0	0		Abs irr	m b g M	view
7	GF(7)	45		+			0	1		Abs irr	m b g M	view
7	GF(49)	56	a	+			0	0		Abs irr	m b g M	view
7	GF(49)	56	b	+			0	0		Abs irr	m b g M	view
7	GF(7)	75		+			1	0		Abs irr	m b g M	view
7	GF(7)	77	a	+			0	0		Abs irr	m b g M	view
7	GF(49)	77	b	+			0	0		Abs irr	m b g M	view
7	GF(49)	77	c	+			0	0		Abs irr	m b g M	view
7	GF(7)	89		+			0	0		Abs irr	m b g M	view
7	GF(7)	112					0	0		Irr not abs irr	m b g M	view
7	GF(7)	120		+			0	0		Abs irr	m b g M	view
7	GF(7)	133	a	+			0	0		Abs irr	m b g M	view
7	GF(49)	133	b	+			0	0		Abs irr	m b g M	view
7	GF(49)	133	c	+			0	0		Abs irr	m b g M	view
7	GF(7)	154					0	0		Irr not abs irr	m b g M	view
7	GF(7)	266					0	0		Irr not abs irr	m b g M	view
Char	Ring	Dim	ID	Ind	Character	Char Rng	H1	H2	Schur	Irr	Files
11	GF(11)	7		+			0	0		Abs irr	m b g M	view
11	GF(11)	14		+			0	1		Abs irr	m b g M	view
11	GF(11)	27		+			0	0		Abs irr	m b g M	view
11	GF(11)	49		+			0	0		Abs irr	m b g M	view
11	GF(11)	56		+			0	0		Abs irr	m b g M	view
11	GF(11)	64		+			0	0		Abs irr	m b g M	view
11	GF(11)	69		+			0	0		Abs irr	m b g M	view
11	GF(11)	77	a	+			0	0		Abs irr	m b g M	view
11	GF(11)	77	b	+			0	0		Abs irr	m b g M	view
11	GF(11)	77	c	+			0	0		Abs irr	m b g M	view
11	GF(11)	106		+			0	0		Abs irr	m b g M	view
11	GF(11)	119		+			1	0		Abs irr	m b g M	view
11	GF(11)	209		+			0	0		Abs irr	m b g M	view
Char	Ring	Dim	ID	Ind	Character	Char Rng	H1	H2	Schur	Irr	Files
19	GF(19)	22		+			0	1		Abs irr	m b g M	view
19	GF(19)	34		+			0	0		Abs irr	m b g M	view
19	GF(19)	43		+			0	0		Abs irr	m b g M	view
19	GF(19)	55		+			1	0		Abs irr	m b g M	view
19	GF(19)	76	a	+			0	0		Abs irr	m b g M	view
19	GF(19)	76	b	+			0	0		Abs irr	m b g M	view
19	GF(19)	77		+			0	0		Abs irr	m b g M	view
19	GF(19)	133	a	+			0	0		Abs irr	m b g M	view
19	GF(19)	133	b	+			0	0		Abs irr	m b g M	view
19	GF(19)	133	c	+			0	0		Abs irr	m b g M	view
19	GF(19)	209		+			0	0		Abs irr	m b g M	view

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Sporadic groups
J₁
Representations of J1

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