C₂₃×#2873 #15670492

order	2944
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₂₃ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂₃×#2873

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂⁴
commutator	C₂	C₂²×C₄²×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂³×C₄
prime radical	C₂⁴×C₂₃	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ G

564 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 736

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#9387, C₂₃×#9388, C₂₃×#9491, …
maximal normal subgroup of	C₂₃×#9387, C₂₃×#9388, C₂₃×#9491, …
maximal quotient of	C₂₃×#17314, C₂₃×#17319, C₂₃×#17324, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1605);

C23×#2873 #15670492