C₂₃×#1561 #15669180

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1510
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#1561

Subgroups

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

210 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 96 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) = 39
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 3 generators on 39 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,29)(26,27)(30,31)(32,33,36,38,37,34,35,39);(24,25,28,30)(26,29,27,31)(32,34)(33,37)(35,39)(36,38);(24,26,28,27)(25,29,30,31)(32,35,37,36)(33,38,34,39)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8472, C₂₃×#8473, C₂₃×#8474, …
maximal normal subgroup of	C₂₃×#8472, C₂₃×#8473, C₂₃×#8474, …
maximal quotient of	C₂₃×#7598, C₂₃×#7602, C₂₃×#7632, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 293);