C₂₃×#2221 #15669840

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

Aliases

direct product

C₂₃×#2221

Subgroups

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

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

normal subgroups only

This group has 148 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) = 55
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 3 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,31)(26,37)(27,32)(28,29)(33,48)(34,45)(35,44)(36,46)(38,52)(39,42)(40,41)(43,49)(50,55)(51,54);(24,25,32,45,29,35,41,46,30,36,40,44,28,34,27,31)(26,33,47,48,37,49,52,54,39,50,53,55,42,51,38,43);(24,26)(25,33)(27,38)(28,42)(29,37)(30,39)(31,43)(32,47)(34,51)(35,49)(36,50)(40,53)(41,52)(44,55)(45,48)(46,54)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#13669, C₂₃×#13670, C₂₃×#13700, …
maximal normal subgroup of	C₂₃×#13669, C₂₃×#13670, C₂₃×#13700, …
maximal quotient of	C₂₃×#12430, C₂₃×#12433, C₂₃×#12439, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 953);