C₂₃×#3039 #15670658

order	2944
nilpotency class	3
isoclinism	isoclinic class of #3003
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₃×#3039

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
prime radical	C₂×#41×C₂₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

480 conjugacy classes of subgroups; only the 208 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 208 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)(28,29,33,37)(30,38,40,43)(31,36,32,35)(34,41,42,39);(24,25,26,27);(28,30)(29,34)(31,39)(32,41)(33,40)(35,38)(36,43)(37,42);(28,31,33,32)(29,35,37,36)(30,39,40,41)(34,38,42,43)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#9171, C₂₃×#9172, C₂₃×#9316, …
maximal normal subgroup of	C₂₃×#9171, C₂₃×#9172, C₂₃×#9316, …
maximal quotient of	C₂₃×#19270, C₂₃×#19271, C₂₃×#19272, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1771);