C₂₃×#2231 #15669850

order	2944
nilpotency class	4
isoclinism	isoclinic class of #2230
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂₃×#2231

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	#476
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

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

normal subgroups only

This group has 120 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)(24,25,30,35)(26,36,39,34)(27,40)(28,44,37,33)(29,31,46,48)(32,49)(38,52)(41,54)(42,53)(43,47)(45,50)(51,55);(24,26,37,46,30,39,28,29)(25,31,44,34,35,48,33,36)(27,38,42,55,43,49,41,45)(32,47,51,53,52,40,50,54);(24,27)(25,32)(26,38)(28,41)(29,45)(30,43)(31,47)(33,50)(34,53)(35,52)(36,54)(37,42)(39,49)(40,48)(44,51)(46,55)

Conjugacy classes & character table

529 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12463, C₂₃×#12464, C₂₃×#12465, …
maximal normal subgroup of	C₂₃×#12463, C₂₃×#12464, C₂₃×#12465, …
maximal quotient of	C₂₃×#12824, C₂₃×#12950, C₂₃×#13116, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 963);