C₂₃×#2102 #15669721

order	2944
nilpotency class	3
isoclinism	isoclinic class of #2031
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂₃×#2102

Subgroups

	subgroup	G/H
center	C₄×C₂₃	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
socle	C₂×C₂₃	#400
prime radical	C₂³×C₂₃	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

158 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 72 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)(24,25,28,27,29,31,33,37)(26,32,34,39,35,36,38,30);(24,26,33,34,29,35,28,38)(25,30,37,32,31,39,27,36);(24,27,28,31,29,37,33,25)(26,32,34,39,35,36,38,30)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7440, C₂₃×#7441, C₂₃×#12307, …
maximal normal subgroup of	C₂₃×#7440, C₂₃×#7441, C₂₃×#12307, …
maximal quotient of	C₂₃×#10687, C₂₃×#10688, C₂₃×#10689, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 834);