C₂₃×#2192 #15669811

order	2944
nilpotency class	4
isoclinism	isoclinic class of #2192
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#2192

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	#447
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂×C₄×C₂₃ ◁ C₂₃×#131 ◁ G

220 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 64 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)(24,25)(26,37)(27,41)(28,35)(29,34)(30,36)(31,38)(32,39)(33,44)(40,52)(42,53)(43,47)(45,51)(46,50)(48,55)(49,54);(24,26)(25,31)(27,42)(28,39)(29,46)(30,40)(32,47)(33,50)(34,48)(35,53)(36,49)(37,41)(38,44)(43,54)(45,55)(51,52);(24,26)(25,32)(27,38)(28,46)(29,39)(30,40)(31,47)(33,49)(34,52)(35,37)(36,50)(41,53)(42,44)(43,55)(45,54)(48,51)

Conjugacy classes & character table

529 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#2192, C₂₃×#33538, C₂₃×#33539, …
maximal normal subgroup of	C₂×C₂₃×#2192, C₂₃×#33538, C₂₃×#33539, …
maximal quotient of	C₂₃×#12108, C₂₃×#12110, C₂₃×#12164, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 924);