C₂₃×#2214 #15669833

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

Aliases

direct product

C₂₃×#2214

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	#459
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₃
prime radical	C₂₃×#135	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂×C₄×C₂₃ ◁ C₄×C₈×C₂₃ ◁ G

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

normal subgroups only

This group has 150 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)(24,25,31,37)(26,35,40,46)(27,41,43,54)(28,36,30,34)(29,32,39,47)(33,48,50,38)(42,55,45,51)(44,52,53,49);(24,26,30,39,31,40,28,29)(25,32,36,46,37,47,34,35)(27,38,45,53,43,48,42,44)(33,41,52,55,50,54,49,51);(24,27)(25,33)(26,38)(28,42)(29,44)(30,45)(31,43)(32,41)(34,49)(35,51)(36,52)(37,50)(39,53)(40,48)(46,55)(47,54)

Conjugacy classes & character table

529 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12312, C₂₃×#12313, C₂₃×#12315, …
maximal normal subgroup of	C₂₃×#12312, C₂₃×#12313, C₂₃×#12315, …
maximal quotient of	C₂₃×#12422, C₂₃×#12423, C₂₃×#12426, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 946);