C₂₃×#3444 #15671063

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₃ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂₃×#3444

Subgroups

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

1212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 5 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);(33,36)(37,39);(32,34,35,38)(33,37,36,39);(24,26,27,30)(25,29,28,31)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#12719, C₂₃×#17458, C₂₃×#17462, …
maximal normal subgroup of	C₂₃×#12719, C₂₃×#17458, C₂₃×#17462, …
maximal quotient of	C₂₃×#34012, C₂₃×#34026, C₄×C₂₃×#525, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2176);

C23×#3444 #15671063