C₂₃×#2370 #15669989

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

Aliases

direct product

C₂₃×#2370

Subgroups

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

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 2944

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#22966, C₂₃×#22967, C₂₃×#22972, …
maximal normal subgroup of	C₂₃×#22966, C₂₃×#22967, C₂₃×#22972, …
maximal quotient of	C₂₃×#13804, C₂₃×#13818, C₂₃×#13819, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1102);

C23×#2370 #15669989