C₂₃×#2212 #15669831

order	2944
nilpotency class	4
isoclinism	isoclinic class of #2212
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#2212

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	#459
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₃
prime radical	C₂₃×#509	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂×C₄×C₂₃ ◁ C₄×C₈×C₂₃ ◁ G

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

normal subgroups only

This group has 154 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)(24,25)(26,34)(27,39)(28,43)(29,45)(30,35)(31,37)(32,36)(33,44)(38,52)(40,51)(41,55)(42,47)(46,48)(49,53)(50,54);(24,26,28,37,30,38,44,29)(25,31,33,34,35,45,43,52)(27,36,40,53,42,54,41,46)(32,47,48,51,50,39,49,55);(24,27)(25,32)(26,36)(28,40)(29,46)(30,42)(31,47)(33,48)(34,51)(35,50)(37,53)(38,54)(39,45)(41,44)(43,49)(52,55)

Conjugacy classes & character table

529 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#2212, C₂₃×#33594, C₂₃×#33595, …
maximal normal subgroup of	C₂×C₂₃×#2212, C₂₃×#33594, C₂₃×#33595, …
maximal quotient of	C₂₃×#12416, C₂₃×#12417, C₂₃×#12420, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 944);