C₂₃×#1624 #15669243

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1619
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₂₃×#1624

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₂₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄²×C₂₃ ◁ G

240 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 1472

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

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7519, C₂₃×#13681, C₂×C₂₃×#1624, …
maximal normal subgroup of	C₂₃×#7519, C₂₃×#13681, C₂×C₂₃×#1624, …
maximal quotient of	C₂₃×#7742, C₂₃×#7743, C₂₃×#7746, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 356);