C₂×C₂₃×#432 #15670537

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×C₂₃×#432

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂³
commutator	C₂²	C₂³×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
socle	C₂³×C₂₃	C₂²×C₄
prime radical	C₂⁴×C₂₃	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ G

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 4 generators on 41 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41);(3,4)(5,8)(6,7)(9,10)(11,12,13,16,14,15,17,18);(4,7)(8,10);(3,5,6,9)(4,8,7,10)(12,15)(16,18)

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#7863, C₂₃×#7864, C₂₃×#7875, …
maximal normal subgroup of	C₂₃×#7863, C₂₃×#7864, C₂₃×#7875, …
maximal quotient of	C₂×C₂₃×#1745, C₂×C₂₃×#1749, C₂×C₂₃×#1767, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1650);

C2×C23×#432 #15670537