Representations of M₂₃

Permutation Representations

Points	ID	Prim	Trans	Rank	Suborbits	Char	Stab	Files
23		Primitive	4	2	1, 22	1 + 22	M22	m b g M	view
253	a	Primitive	1	3	1, 42, 210	1 + 22 + 230	L3(4):22	m b g M	view
253	b	Primitive	1	3	1, 112, 140	1 + 22 + 230	24:A7	m b g M	view
506		Primitive	1	4	1, 15, 210, 280	1 + 22 + 230 + 253	A8	m b g M	view
1288		Primitive	1	4	1, 165, 330, 792	1 + 22 + 230 + 1035	M11	m b g M	view
1771		Primitive	1	8	1, 20, 60, 90, 160, 4803	1 + 22 + 2.230 + 253 + 1035	24:(3 × A5):2	m b g M	view
40320		Primitive	1	164	1, 234, 253159		23:11	m b g M	view

Matrix Representations

Char	Ring	Dim	ID	Ind	Character	Char Rng	H1	H2	Schur	Irr	Files
0	Z	22		+	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	Z	230		+	χ5	Z			1	Abs irr	m b g M	view
0	Z	231	a	+	χ6	Z			1	Abs irr	m b g M	view
0	Q(b15)	231	b	o	χ7	Z[b15]			1	Abs irr	m b g M	view
0	Q(b15)	231	c	o	χ7	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							Abs irr	m b g M	view
2	GF(2)	11	b							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(4)	896	a							Abs irr	m b g M	view
2	GF(4)	896	b							Abs irr	m b g M	view
Char	Ring	Dim	ID	Ind	Character	Char Rng	H1	H2	Schur	Irr	Files
3	GF(3)	22								Abs irr	m b g M	view
3	GF(9)	45	b							Abs irr	m b g M	view
3	GF(3)	104	a							Abs irr	m b g M	view
3	GF(3)	104	b							Abs irr	m b g M	view
3	GF(3)	231								Abs irr	m b g M	view
3	GF(3)	253								Abs irr	m b g M	view
3	GF(3)	770	a							Abs irr	m b g M	view
3	GF(9)	990	b							Abs irr	m b g M	view
Char	Ring	Dim	ID	Ind	Character	Char Rng	H1	H2	Schur	Irr	Files
5	GF(5)	22								Abs irr	m b g M	view
5	GF(25)	45	a							Abs irr	m b g M	view
5	GF(5)	230								Abs irr	m b g M	view
5	GF(5)	231	a							Abs irr	m b g M	view
5	GF(5)	231	b							Abs irr	m b g M	view
5	GF(25)	770								Abs irr	m b g M	view
5	GF(5)	896	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)	22								Abs irr	m b g M	view
7	GF(7)	45								Abs irr	m b g M	view
7	GF(7)	208								Abs irr	m b g M	view
7	GF(7)	231	a							Abs irr	m b g M	view
7	GF(49)	231	b							Abs irr	m b g M	view
7	GF(49)	231	c							Abs irr	m b g M	view
7	GF(49)	770	a							Abs irr	m b g M	view
7	GF(49)	770	b							Abs irr	m b g M	view
7	GF(49)	896	a							Abs irr	m b g M	view
7	GF(49)	896	b							Abs irr	m b g M	view
7	GF(7)	990	a							Abs irr	m b g M	view
Char	Ring	Dim	ID	Ind	Character	Char Rng	H1	H2	Schur	Irr	Files
11	GF(11)	22								Abs irr	m b g M	view
11	GF(11)	45	b							Abs irr	m b g M	view
11	GF(11)	229								Abs irr	m b g M	view
11	GF(11)	231	a							Abs irr	m b g M	view
11	GF(121)	231	b							Abs irr	m b g M	view
11	GF(121)	231	c							Abs irr	m b g M	view
11	GF(11)	253								Abs irr	m b g M	view
11	GF(121)	770	a							Abs irr	m b g M	view
11	GF(121)	770	b							Abs irr	m b g M	view
11	GF(11)	806								Abs irr	m b g M	view
11	GF(11)	990	a							Abs irr	m b g M	view
Char	Ring	Dim	ID	Ind	Character	Char Rng	H1	H2	Schur	Irr	Files
23	GF(23)	21								Abs irr	m b g M	view
23	GF(23)	45	b							Abs irr	m b g M	view
23	GF(23)	210								Abs irr	m b g M	view
23	GF(23)	230								Abs irr	m b g M	view
23	GF(23)	231	a							Abs irr	m b g M	view
23	GF(23)	253								Abs irr	m b g M	view
23	GF(23)	280								Abs irr	m b g M	view
23	GF(23)	665	b							Abs irr	m b g M	view

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