C₂₃×#1460 #15669079

order	2944
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₂₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₂₃×#1460

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²⋊C₄
commutator	C₂²	C₂²×C₈×C₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
socle	C₂²×C₂₃	C₂×C₂²⋊C₄
prime radical	C₂²×D₄×C₂₃	C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

312 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 124 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) = 736

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)(24,25,26,29,27,28,30,31)(32,33,35,38,36,39,34,37);(25,28)(26,30);(32,34,36,35)(33,37,39,38)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7204, C₂₃×#7285, C₈×C₂₃×#100, …
maximal normal subgroup of	C₂₃×#7204, C₂₃×#7285, C₈×C₂₃×#100, …
maximal quotient of	C₂₃×#7567, C₂₃×#7569, C₂₃×#7571, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 192);