C₂₃×#2188 #15669807

order	2944
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#2188

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₃
prime radical	C₂³×C₂₃	D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ C₂²×C₈×C₂₃ ◁ G

216 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 59
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 3 generators on 59 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)(26,27)(28,29,33,37)(30,38,41,57)(31,42,46,56)(32,47,44,36)(34,49,51,39)(35,52,54,45)(40,58,48,53)(43,55,59,50);(28,30,33,41)(29,34,37,51)(31,43,46,59)(32,48,44,40)(35,53,54,58)(36,55,47,50)(38,56,57,42)(39,52,49,45);(25,27)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12106, C₂₃×#12107, C₂₃×#12112, …
maximal normal subgroup of	C₂₃×#12106, C₂₃×#12107, C₂₃×#12112, …
maximal quotient of	C₂₃×#12106, C₂₃×#12162, C₂₃×#12282, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 920);