C₉×#2214 #11766935

order	1152
nilpotency class	4
isoclinism	isoclinic class of #2212
automorphism	?
homology	Abelianization (H₁) = C₂³×C₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₉×#2214

Subgroups

	subgroup	G/H
center	C₂×C₉	#459
commutator	C₂×C₈	C₂³×C₉
Frattini, cosocle	C₂×C₃×C₈	C₂³×C₃
socle	C₂×C₃	C₃×#459
prime radical	C₃×#135	C₂²×C₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₉ ◁ C₂×C₄×C₉ ◁ C₄×C₈×C₉ ◁ G

225 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 225 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 41
transitive degree	μ_t(G) = 288

A minimal faithful permutation representation — 3 generators on 41 points:

(1,2,3,4,5,6,7,8,9)(10,11,17,23)(12,21,26,32)(13,27,29,40)(14,22,16,20)(15,18,25,33)(19,34,36,24)(28,41,31,37)(30,38,39,35);(10,12,16,25,17,26,14,15)(11,18,22,32,23,33,20,21)(13,24,31,39,29,34,28,30)(19,27,38,41,36,40,35,37);(10,13)(11,19)(12,24)(14,28)(15,30)(16,31)(17,29)(18,27)(20,35)(21,37)(22,38)(23,36)(25,39)(26,34)(32,41)(33,40)

Conjugacy classes & character table

207 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 946);