C₂₃×#2273 #15669892

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×#2273

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁴
commutator	C₂	C₂²×C₄²×C₂₃
Frattini, cosocle	C₂³	C₂⁴×C₂₃
prime radical	C₂⁵×C₂₃	C₂²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

912 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)(28,29,31,30)(32,33)(34,38)(35,36)(37,39);(24,25,26,27)(28,30,31,29)(33,36)(37,38);(32,33)(34,37)(35,36)(38,39);(32,34)(33,37)(35,39)(36,38)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#8734, C₂₃×#9407, C₂₃×#9409, …
maximal normal subgroup of	C₂₃×#8734, C₂₃×#9407, C₂₃×#9409, …
maximal quotient of	C₂₃×#13749, C₂₃×#13775, C₂₃×#13778, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1005);

C23×#2273 #15669892