C₂₃×#1762 #15669381

order	2944
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₃ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂₃×#1762

Subgroups

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

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

normal subgroups only

This group has 388 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) = 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)(24,25)(26,27)(28,29,31,30)(33,37)(34,35)(38,39);(25,27)(32,33,35,39,36,38,34,37);(28,30,31,29)(33,38)(37,39)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8416, C₂₃×#8418, C₂₃×#9163, …
maximal normal subgroup of	C₂₃×#8416, C₂₃×#8418, C₂₃×#9163, …
maximal quotient of	C₂₃×#8170, C₂₃×#8172, C₂₃×#8179, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 494);