C₂₃×#2344 #15669963

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

Aliases

direct product

C₂₃×#2344

Subgroups

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

604 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 4 generators on 39 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)(28,29,30,31)(34,38)(36,39);(25,26)(32,33,35,37)(34,36,38,39);(32,34)(33,36)(35,38)(37,39);(24,26,27,25)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#9256, C₂₃×#9260, C₂₃×#22406, …
maximal normal subgroup of	C₂₃×#9256, C₂₃×#9260, C₂₃×#22406, …
maximal quotient of	C₂₃×#13799, C₂²⋊C₄×C₄⋊C₄×C₂₃, C₂₃×#13810, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1076);

C23×#2344 #15669963