C₂₃×#2213 #15669832

order	2944
nilpotency class	4
isoclinism	isoclinic class of #2212
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#2213

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	#459
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂×C₄×C₂₃ ◁ C₄×C₈×C₂₃ ◁ G

170 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 368

A minimal faithful permutation representation — 3 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)(25,28)(26,31)(27,29)(32,33)(34,39)(35,38)(36,37);(24,25,29,32,30,33,27,28)(26,31,37,39,35,38,34,36);(24,26)(25,31)(27,34)(28,36)(29,37)(30,35)(32,39)(33,38)

Conjugacy classes & character table

529 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12310, C₂₃×#12311, C₂₃×#12314, …
maximal normal subgroup of	C₂₃×#12310, C₂₃×#12311, C₂₃×#12314, …
maximal quotient of	C₂₃×#12418, C₂₃×#12419, C₂₃×#12424, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 945);