C₂₃×#2251 #15669870

order	2944
nilpotency class	4
isoclinism	isoclinic class of #2218
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₂₃×#2251

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

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

normal subgroups only

This group has 178 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)(25,27)(28,29,33,37)(30,38,40,52)(31,43,45,58)(32,46,44,36)(34,47,48,41)(35,50,51,39)(42,57,56,54)(49,55,53,59);(28,30,39,55,32,42,45,47,33,40,50,59,44,56,31,41)(29,34,43,54,36,49,51,52,37,48,58,57,46,53,35,38);(24,25,26,27)(30,40)(34,48)(38,52)(41,47)(42,56)(49,53)(54,57)(55,59)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12326, C₂₃×#12327, C₂₃×#12338, …
maximal normal subgroup of	C₂₃×#12326, C₂₃×#12327, C₂₃×#12338, …
maximal quotient of	C₂₃×#12507, C₂₃×#12508, C₂₃×#12512, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 983);