C₂₃×#1773 #15669392

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

Aliases

direct product

C₂₃×#1773

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂×D₄
commutator	C₄	C₂×C₄²×C₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
socle	C₂²×C₂₃	C₄×D₄
prime radical	C₂³×C₂₃	#41
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂²×C₈×C₂₃ ◁ G

224 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 152 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) = 43
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 3 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(29,33,35,38)(30,36)(34,41,42,40)(37,43);(24,25,26,27)(28,29)(30,34)(31,38)(32,35)(33,39)(36,42)(37,41)(40,43);(28,30,31,37,32,36,39,43)(29,34,38,41,35,42,33,40)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12647, C₂₃×#12648, C₂₃×#12649, …
maximal normal subgroup of	C₂₃×#12647, C₂₃×#12648, C₂₃×#12649, …
maximal quotient of	C₂₃×#8268, C₂₃×#8269, C₂₃×#8270, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 505);