C₂₃×#2191 #15669810

order	2944
nilpotency class	4
isoclinism	isoclinic class of #2190
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#2191

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	#447
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₃
prime radical	C₂₃×#575	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂×C₄×C₂₃ ◁ C₂×M₁₆×C₂₃ ◁ G

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

normal subgroups only

This group has 216 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)(24,25,29,33)(26,34,36,52)(27,38,40,54)(28,43,41,32)(30,45,46,35)(31,48,50,42)(37,53,44,49)(39,51,55,47);(24,26)(25,30)(27,39)(28,44)(29,36)(31,49)(32,51)(33,46)(34,38)(35,42)(37,41)(40,55)(43,47)(45,48)(50,53)(52,54);(27,40)(31,50)(34,52)(35,45)(38,54)(39,55)(42,48)(49,53)

Conjugacy classes & character table

460 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12115, C₂₃×#12116, C₂₃×#12118, …
maximal normal subgroup of	C₂₃×#12115, C₂₃×#12116, C₂₃×#12118, …
maximal quotient of	C₂₃×#12105, C₂₃×#12106, C₂₃×#12107, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 923);