C₂₃×#2920 #15670539

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

Aliases

direct product

C₂₃×#2920

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	C₂⁴×C₂₃	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₂₃ ◁ G

484 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)(26,29)(27,28)(30,31)(32,33,34,37,35,36,38,39);(25,28)(29,31);(24,26,27,30)(25,29,28,31);(33,36)(37,39)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#7855, C₂₃×#7856, C₂₃×#7857, …
maximal normal subgroup of	C₂₃×#7855, C₂₃×#7856, C₂₃×#7857, …
maximal quotient of	C₂₃×#20364, C₄×C₂₃×#407, C₄×C₂₃×#423, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1652);

C23×#2920 #15670539