C₂₃×#3189 #15670808

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

Aliases

direct product

C₂₃×#3189

Subgroups

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

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

normal subgroups only

This group has 416 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) = 736

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

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#9276, C₂₃×#9955, C₂₃×#9957, …
maximal normal subgroup of	C₂₃×#9276, C₂₃×#9955, C₂₃×#9957, …
maximal quotient of	C₂₃×#21759, C₂₃×#21940, C₂₃×#22044, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1921);