C₂₃×#2298 #15669917

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

Aliases

direct product

C₂₃×#2298

Subgroups

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

524 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 1472

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)(24,25,27,26)(28,29)(30,33)(31,32)(34,35)(36,37)(38,41)(39,40)(42,43);(24,26,27,25)(29,32)(33,35);(28,30,31,34)(29,33,32,35)(37,40)(41,43);(36,38,39,42)(37,41,40,43)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#8732, C₂₃×#8733, C₂₃×#8740, …
maximal normal subgroup of	C₂₃×#8732, C₂₃×#8733, C₂₃×#8740, …
maximal quotient of	C₂₃×#13757, C₂₃×#13759, C₂₃×#13761, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1030);

C23×#2298 #15669917