C₂₃×#1998 #15669617

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₂₃×#1998

Subgroups

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

228 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 112 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) = 47
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 3 generators on 47 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)(26,30)(27,28)(29,31)(32,33,36,39,35,38,40,46)(34,37,42,45,41,44,43,47);(25,28)(29,30)(32,34,40,42,35,41,36,43)(33,37,39,47,38,44,46,45);(24,26,27,31)(25,29,28,30)(33,38)(37,44)(39,46)(45,47)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8485, C₂₃×#8486, C₂₃×#10497, …
maximal normal subgroup of	C₂₃×#8485, C₂₃×#8486, C₂₃×#10497, …
maximal quotient of	C₂₃×#9880, C₂₃×#9881, C₂₃×#9892, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 730);