C₂₃×#2646 #15670265

order	2944
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#2646

Subgroups

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

436 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 200 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) = 47
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 4 generators on 47 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,28,29)(26,27,30,31)(33,34)(37,38)(40,41)(42,45)(43,46)(44,47);(25,29)(26,30)(32,33,36,34)(35,37,39,38)(40,42)(41,44)(43,47)(45,46);(24,26)(25,27)(28,30)(29,31)(32,34,36,33)(35,37,39,38)(40,42)(41,45)(43,47)(44,46);(24,27)(25,30)(26,29)(28,31)(32,35)(33,37)(34,38)(36,39)(40,41)(42,44)(43,46)(45,47)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#10344, C₂₃×#10345, C₂₃×#10346, …
maximal normal subgroup of	C₂₃×#10344, C₂₃×#10345, C₂₃×#10346, …
maximal quotient of	C₂₃×#14265, C₂₃×#14275, C₂₃×#14329, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1378);