C₂₃×#2222 #15669841

order	2944
nilpotency class	4
isoclinism	isoclinic class of #2221
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#2222

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	#466
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₃
prime radical	#41×C₂₃	D₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂×C₄×C₂₃ ◁ C₂₃×#131 ◁ G

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

normal subgroups only

This group has 140 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) = 87
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 3 generators on 87 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,31,37)(26,38,44,66)(27,45,48,62)(28,49,51,60)(29,36,30,35)(32,53,57,41)(33,52,59,47)(34,50,61,39)(40,69,72,86)(42,65,43,64)(46,77,78,58)(54,81,82,87)(55,73,56,67)(63,74,85,71)(68,76,79,84)(70,75,80,83);(24,26,39,67,30,43,51,53,31,44,50,73,29,42,28,41)(25,32,49,65,36,56,61,66,37,57,60,64,35,55,34,38)(27,40,68,87,47,71,78,80,48,72,79,81,52,74,46,70)(33,54,76,69,45,75,77,85,59,82,84,86,62,83,58,63);(24,27)(25,33)(26,40)(28,46)(29,52)(30,47)(31,48)(32,54)(34,58)(35,62)(36,45)(37,59)(38,63)(39,68)(41,70)(42,74)(43,71)(44,72)(49,76)(50,79)(51,78)(53,80)(55,83)(56,75)(57,82)(60,84)(61,77)(64,86)(65,69)(66,85)(67,87)(73,81)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#13671, C₂₃×#13672, C₂₃×#13701, …
maximal normal subgroup of	C₂₃×#13671, C₂₃×#13672, C₂₃×#13701, …
maximal quotient of	C₂₃×#12431, C₂₃×#12434, C₂₃×#12440, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 954);