C₂₃×#2276 #15669895

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×#2276

Subgroups

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

628 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 2944

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#9324, C₂₃×#9326, C₂₃×#17549, …
maximal normal subgroup of	C₂₃×#9324, C₂₃×#9326, C₂₃×#17549, …
maximal quotient of	C₂₃×#13750, C₂₃×#13783, C₂₃×#13786, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1008);

C23×#2276 #15669895