C₂₃×#2327 #15669946

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₃×#2327

Subgroups

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

516 conjugacy classes of subgroups; only the 296 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 296 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) = 2944

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)(25,27)(28,29,31,30)(33,37)(34,40)(35,43)(45,47);(28,30,31,29)(32,33)(34,41)(35,39)(36,37)(38,40)(42,47)(43,44)(45,46);(24,25,26,27)(32,34)(33,38)(35,42)(36,40)(37,41)(39,45)(43,46)(44,47);(32,35,36,43)(33,39,37,44)(34,42,40,46)(38,45,41,47)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#9100, C₂₃×#9104, C₂₃×#9296, …
maximal normal subgroup of	C₂₃×#9100, C₂₃×#9104, C₂₃×#9296, …
maximal quotient of	C₂₃×#13779, C₂₃×#13786, C₂₃×#13790, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1059);