C₂₃×#2974 #15670593

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

Aliases

direct product

C₂₃×#2974

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂³×C₄
prime radical	C₂²×D₄×C₂₃	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ G

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 736

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#9163, C₂₃×#9165, C₂₃×#9243, …
maximal normal subgroup of	C₂₃×#9163, C₂₃×#9165, C₂₃×#9243, …
maximal quotient of	C₂₃×#20525, C₂₃×#20535, C₂₃×#20558, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1706);

C23×#2974 #15670593