C₂₃×#2921 #15670540

order	2944
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂₃×#2921

Subgroups

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

392 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 264 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) = 47
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 4 generators on 47 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)(32,33,35,39,36,38,42,45)(34,37,41,44,40,43,46,47);(25,28)(29,31)(32,34)(33,37)(35,41)(36,40)(38,43)(39,44)(42,46)(45,47);(24,26,27,30)(25,29,28,31)(34,40)(37,43)(41,46)(44,47);(33,38)(37,43)(39,45)(44,47)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8863, C₂₃×#9034, C₂₃×#9036, …
maximal normal subgroup of	C₂₃×#8863, C₂₃×#9034, C₂₃×#9036, …
maximal quotient of	C₂₃×#20365, C₂₃×#20377, C₂₃×#20429, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1653);