C₂₃×#2880 #15670499

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₃×#2880

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂³×C₄
prime radical	C₂²×#41×C₂₃	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ G

774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 4 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25)(26,27)(28,29,31,34,32,35,38,41)(30,33,37,40,36,39,42,43);(25,27);(28,30)(29,33)(31,37)(32,36)(34,40)(35,39)(38,42)(41,43);(30,36)(33,39)(37,42)(40,43)

Conjugacy classes & character table

1150 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#9239, C₂₃×#9241, C₂₃×#9345, …
maximal normal subgroup of	C₂₃×#9239, C₂₃×#9241, C₂₃×#9345, …
maximal quotient of	C₂₃×#17411, C₂₃×#17412, C₂₃×#17413, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1612);

C23×#2880 #15670499