C₂₃×#1853 #15669472

order	2944
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#1853

Subgroups

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

360 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 144 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)(32,33,35,38)(34,36,39,37);(28,30,31,29)(33,36)(34,39)(37,38);(25,27)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8854, C₂₃×#8855, C₂₃×#8857, …
maximal normal subgroup of	C₂₃×#8854, C₂₃×#8855, C₂₃×#8857, …
maximal quotient of	C₂₃×#8830, C₂₃×#8833, C₂₃×#8854, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 585);