C₂₃×#3261 #15670880

order	2944
nilpotency class	3
isoclinism	isoclinic class of #3198
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#3261

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
prime radical	C₂³×C₂₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#117 ◁ G

322 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 168 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) = 63
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 4 generators on 63 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,28)(26,30)(32,33,37,41)(34,38,43,52)(35,45,47,55)(36,48,50,40)(39,49,54,46)(42,56,57,63)(44,60,59,53)(51,61,62,58);(24,25)(26,29)(27,28)(30,31)(32,34,37,43)(33,38,41,52)(35,42,47,57)(36,44,50,59)(39,51,54,62)(40,53,48,60)(45,56,55,63)(46,58,49,61);(25,28)(29,31)(32,35,37,47)(33,39,41,54)(34,42,43,57)(36,49,50,46)(38,51,52,62)(40,55,48,45)(44,61,59,58)(53,63,60,56);(24,26,27,30)(25,29,28,31)(34,43)(38,52)(42,57)(44,59)(51,62)(53,60)(56,63)(58,61)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12165, C₂₃×#12168, C₂₃×#12171, …
maximal normal subgroup of	C₂₃×#12165, C₂₃×#12168, C₂₃×#12171, …
maximal quotient of	C₂₃×#21898, C₂₃×#21968, C₂₃×#22124, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1993);