C₂₃×#3152 #15670771

order	2944
nilpotency class	3
isoclinism	isoclinic class of #3055
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂₃×#3152

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
prime radical	C₂₃×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

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

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 224 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)(25,27)(28,29,32,35)(30,36,37,43)(31,39,40,34)(33,41,42,38);(28,30,31,38,32,37,40,41)(29,33,34,36,35,42,39,43);(24,25,26,27);(30,37)(33,42)(36,43)(38,41)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#9421, C₂₃×#9429, C₂₃×#9435, …
maximal normal subgroup of	C₂₃×#9421, C₂₃×#9429, C₂₃×#9435, …
maximal quotient of	C₂₃×#19622, C₂₃×#19626, C₂₃×#19630, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1884);