C₂₃×#2922 #15670541

order	2944
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂₃×#2922

Subgroups

	subgroup	G/H
center	C₄²×C₂₃	C₂³
commutator	C₂²	C₂³×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂³×C₄
prime radical	C₂×#41×C₂₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₂₃ ◁ G

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 4 generators on 47 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)(26,29)(27,28)(30,31)(32,33,35,38,36,39,42,45)(34,37,41,44,40,43,46,47);(25,28)(29,31)(32,34)(33,37)(35,41)(36,40)(38,44)(39,43)(42,46)(45,47);(24,26,27,30)(25,29,28,31);(34,40)(37,43)(41,46)(44,47)

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#8187, C₂₃×#8188, C₂₃×#8189, …
maximal normal subgroup of	C₂₃×#8187, C₂₃×#8188, C₂₃×#8189, …
maximal quotient of	C₂₃×#20366, C₄×C₂₃×#408, C₄×C₂₃×#424, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1654);

C23×#2922 #15670541