C₂₃×#2211 #15669830

order	2944
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#2211

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₃
prime radical	C₂×D₈×C₂₃	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄²×C₂₃ ◁ C₄×C₈×C₂₃ ◁ G

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

normal subgroups only

This group has 158 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) = 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)(25,27)(28,29)(30,38)(31,34)(32,44)(33,47)(35,40)(36,46)(37,43)(39,54)(41,58)(42,55)(45,53)(48,52)(49,56)(50,57)(51,59);(24,25,26,27)(29,34)(35,49)(36,50)(37,47)(38,54)(44,55)(51,53)(52,58);(28,30,31,39)(29,35,34,49)(32,45,42,59)(33,48,43,41)(36,52,50,58)(37,53,47,51)(38,55,54,44)(40,57,56,46)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#2211, C₂₃×#33579, C₂₃×#33581, …
maximal normal subgroup of	C₂×C₂₃×#2211, C₂₃×#33579, C₂₃×#33581, …
maximal quotient of	C₂₃×#12419, C₂₃×#12423, C₂₃×#12429, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 943);