C₂₃×#3249 #15670868

order	2944
nilpotency class	3
isoclinism	isoclinic class of #3186
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#3249

Subgroups

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

348 conjugacy classes of subgroups; only the 188 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 188 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) = 1472

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

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#10030, C₂₃×#10031, C₂₃×#10195, …
maximal normal subgroup of	C₂₃×#10030, C₂₃×#10031, C₂₃×#10195, …
maximal quotient of	C₂₃×#21885, C₂₃×#21961, C₂₃×#22113, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1981);