Representations of M₂₄

Permutation Representations

Points	ID	Prim	Trans	Rank	Suborbits	Char	Stab	Files
24		Primitive	5	2	1, 23	1 + 23	M23	m b g M	view
276		Primitive	1	3	1, 44, 231	1 + 23 + 252	M22:2	m b g M	view
759		Primitive	1	4	1, 30, 280, 448	1 + 23 + 252 + 483	24:A8 = 24:L4(2)	m b g M	view
1288		Primitive	1	3	1, 495, 792	1 + 252 + 1035a	M12:2	m b g M	view
1771		Primitive	1	4	1, 90, 240, 1440	1 + 252 + 483 + 1035a	26:3.S6	m b g M	view
2024		Primitive	1	5	1, 63, 210, 630, 1120	1 + 23 + 252 + 483 + 1265	L3(4):3:22 = M21:S3	m b g M	view
3795		Primitive	1	5	1, 42, 56, 1008, 2688	1 + 252 + 483 + 1035a + 2024	26:(L3(2) × S3)	m b g M	view

Matrix Representations

Char	Ring	Dim	ID	Ind	Character	Char Rng	H1	H2	Schur	Irr	Files
0	Z	23		+	χ2	Z			1	Abs irr	m b g M	view
0	Z[b7, ½]	45	a	o	χ3	Z[b7]			1	Abs irr	m b g M	view
0	Z[b7, ½]	45	b	o	χ4	Z[b7]			1	Abs irr	m b g M	view
0	Q(b15)	231	a	o	χ5	Z[b15]			1	Abs irr	m b g M	view
0	Q(b15)	231	b	o	χ6	Z[b15]			1	Abs irr	m b g M	view
Char	Ring	Dim	ID	Ind	Character	Char Rng	H1	H2	Schur	Irr	Files
2	GF(2)	11	a	o	φ2	Z[b7, b15, b23]	0	0	1	Abs irr	m b g M	view
2	GF(2)	11	b	o	φ3	Z[b7, b15, b23]	1	1	1	Abs irr	m b g M	view
2	GF(2)	44	a							Abs irr	m b g M	view
2	GF(2)	44	b							Abs irr	m b g M	view
2	GF(2)	120		+						Abs irr	m b g M	view
2	GF(2)	220	a							Abs irr	m b g M	view
2	GF(2)	220	b							Abs irr	m b g M	view
2	GF(2)	252								Abs irr	m b g M	view
2	GF(2)	320	a							Abs irr	m b g M	view
2	GF(2)	320	b							Abs irr	m b g M	view
2	GF(2)	1242								Abs irr	m b g M	view
2	GF(2)	1792								Abs irr	m b g M	view
Char	Ring	Dim	ID	Ind	Character	Char Rng	H1	H2	Schur	Irr	Files
3	GF(3)	22		+	φ2	Z	1	1	1	Abs irr	m b g M	view
3	GF(9)	45	a	o	φ3	Z[b7]	0	0	1	Abs irr	m b g M	view
3	GF(9)	45	b	o	φ4	Z[b7]	0	0	1	Abs irr	m b g M	view
3	GF(3)	231		+	φ5	Z	0		1	Abs irr	m b g M	view
3	GF(3)	252		+	φ6	Z	0		1	Abs irr	m b g M	view
3	GF(3)	483		+	φ7	Z	0		1	Abs irr	m b g M	view
3	GF(3)	770	a	o	φ8	Z[b23]			1	Abs irr	m b g M	view
3	GF(3)	770	b	o	φ9	Z[b23]			1	Abs irr	m b g M	view
3	GF(9)	990	b	o	φ11	Z[b7]	0	0	1	Abs irr	m b g M	view
Char	Ring	Dim	ID	Ind	Character	Char Rng	H1	H2	Schur	Irr	Files
5	GF(5)	23								Abs irr	m b g M	view
5	GF(25)	45	a							Abs irr	m b g M	view
5	GF(25)	45	b							Abs irr	m b g M	view
5	GF(5)	231								Abs irr	m b g M	view
5	GF(5)	252								Abs irr	m b g M	view
5	GF(5)	253								Abs irr	m b g M	view
5	GF(25)	770	a							Abs irr	m b g M	view
5	GF(25)	990	a							Abs irr	m b g M	view
Char	Ring	Dim	ID	Ind	Character	Char Rng	H1	H2	Schur	Irr	Files
7	GF(7)	23								Abs irr	m b g M	view
7	GF(7)	45								Abs irr	m b g M	view
7	GF(49)	231	b							Abs irr	m b g M	view
7	GF(7)	252								Abs irr	m b g M	view
7	GF(7)	253								Abs irr	m b g M	view
7	GF(7)	483								Abs irr	m b g M	view
7	GF(49)	770	a							Abs irr	m b g M	view
7	GF(7)	990								Abs irr	m b g M	view
Char	Ring	Dim	ID	Ind	Character	Char Rng	H1	H2	Schur	Irr	Files
11	GF(11)	23								Abs irr	m b g M	view
11	GF(11)	45								Abs irr	m b g M	view
11	GF(11)	229								Abs irr	m b g M	view
11	GF(121)	231	b							Abs irr	m b g M	view
11	GF(11)	253								Abs irr	m b g M	view
11	GF(11)	482								Abs irr	m b g M	view
11	GF(121)	770	a							Abs irr	m b g M	view
11	GF(11)	806								Abs irr	m b g M	view
11	GF(11)	990	b							Abs irr	m b g M	view
Char	Ring	Dim	ID	Ind	Character	Char Rng	H1	H2	Schur	Irr	Files
23	GF(23)	23								Abs irr	m b g M	view
23	GF(23)	45								Abs irr	m b g M	view
23	GF(23)	231	b							Abs irr	m b g M	view
23	GF(23)	251								Abs irr	m b g M	view
23	GF(23)	253								Abs irr	m b g M	view
23	GF(23)	483								Abs irr	m b g M	view
23	GF(23)	770								Abs irr	m b g M	view
23	GF(23)	990	b							Abs irr	m b g M	view

Version 3.004 / HTML 4.01 / CSS

Navigation

Up

ATLAS index page
Sporadic groups
M₂₄
Representations of M24

Lookup