C₂₃×#2972 #15670591

order	2944
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₃×#2972

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂⁴
commutator	C₂	C₂³×C₈×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂³×C₄
prime radical	C₂²×D₄×C₂₃	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ G

500 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)(32,33,34,36,35,37,38,39);(24,26)(25,28)(27,31)(29,30);(26,31)(28,30);(25,29)(28,30)

Conjugacy classes & character table

1564 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#8835, C₂₃×#8851, C₂₃×#8957, …
maximal normal subgroup of	C₂₃×#8835, C₂₃×#8851, C₂₃×#8957, …
maximal quotient of	C₂₃×#20523, C₂₃×#20533, C₂₃×#20555, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1704);

C23×#2972 #15670591