C₂×C₂₃×#431 #15670536

order	2944
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈×C₂₃ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂×C₂₃×#431

Subgroups

	subgroup	G/H
center	C₂×C₄²×C₂₃	C₂²
commutator	C₂	C₂³×C₈×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
socle	C₂³×C₂₃	C₂²×C₄
prime radical	C₂⁴×C₂₃	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₂₃ ◁ G

528 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)(11,12,13,15,14,16,17,18);(4,7)(8,10);(3,5,6,9)(4,8,7,10)

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#7848, C₂₃×#7849, C₂₃×#7850, …
maximal normal subgroup of	C₂₃×#7848, C₂₃×#7849, C₂₃×#7850, …
maximal quotient of	C₂×C₂₃×#1744, C₂×C₄×C₂₃×C₂²⋊C₈, C₂×C₄×C₂₃×C₄⋊C₈, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1649);

C2×C23×#431 #15670536