C₂₃×#1950 #15669569

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

Aliases

direct product

C₂₃×#1950

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
socle	C₂²×C₂₃	C₂×C₄⋊C₄
prime radical	C₂³×C₂₃	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

200 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 116 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 — 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)(25,27)(28,29,32,35,33,36,31,40)(30,37,38,34,39,42,41,43);(28,30,32,38,33,39,31,41)(29,34,35,42,36,43,40,37);(24,25,26,27)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8906, C₂₃×#8907, C₂₃×#8908, …
maximal normal subgroup of	C₂₃×#8906, C₂₃×#8907, C₂₃×#8908, …
maximal quotient of	C₂₃×#9601, C₂₃×#9602, C₂₃×#9603, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 682);