Finite Group Databasebeta

← Prev (#15669462) Next (#15669464) →

C₂₃×#1844 #15669463

order	2944
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₃	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 2944

A minimal faithful permutation representation — 3 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)(25,27)(28,29,30,31)(33,36)(34,38)(37,39);(32,33,34,36,35,37,38,39);(24,25,26,27)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7268, C₂₃×#7278, C₂₃×#7371, …
maximal normal subgroup of	C₂₃×#7268, C₂₃×#7278, C₂₃×#7371, …
maximal quotient of	C₂₃×#8805, C₂₃×#8809, C₂₃×#8813, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 576);