C₂₃×#2353 #15669972

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

Aliases

direct product

C₂₃×#2353

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁴×C₂₃
prime radical	C₂²×D₄×C₂₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

588 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)(24,25,26,27)(28,29)(30,33)(31,32)(34,35)(36,37)(38,42)(39,41)(40,43);(29,32)(33,35)(36,37,39,41)(38,40,43,42);(28,30,31,34)(29,33,32,35)(36,38)(37,40)(39,43)(41,42);(28,29)(30,33)(31,32)(34,35)(36,37)(38,40)(39,41)(42,43)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#8762, C₂₃×#8763, C₂₃×#8772, …
maximal normal subgroup of	C₂₃×#8762, C₂₃×#8763, C₂₃×#8772, …
maximal quotient of	C₂₃×#13802, C₂₃×#13806, C₂₃×#13807, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1085);

C23×#2353 #15669972