C₂₃×#2379 #15669998

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₂₃×#2379

Subgroups

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

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

normal subgroups only

This group has 520 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) = 43
transitive degree	μ_t(G) = 1472

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

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8910, C₂₃×#8911, C₂₃×#8914, …
maximal normal subgroup of	C₂₃×#8910, C₂₃×#8911, C₂₃×#8914, …
maximal quotient of	C₂₃×#13829, C₂₃×#13831, C₂₃×#13832, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1111);