C₉×#2192 #11766913

order	1152
nilpotency class	4
isoclinism	isoclinic class of #2192
automorphism	?
homology	Abelianization (H₁) = C₂³×C₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₉×#2192

Subgroups

	subgroup	G/H
center	C₂×C₉	#447
commutator	C₂×C₈	C₂³×C₉
Frattini, cosocle	C₂×C₃×C₈	C₂³×C₃
socle	C₂×C₃	C₃×#447
prime radical	C₃×#2192	C₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₉ ◁ C₂×C₄×C₉ ◁ C₉×#131 ◁ G

330 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 96 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)(12,23)(13,27)(14,21)(15,20)(16,22)(17,24)(18,25)(19,30)(26,38)(28,39)(29,33)(31,37)(32,36)(34,41)(35,40);(10,12)(11,17)(13,28)(14,25)(15,32)(16,26)(18,33)(19,36)(20,34)(21,39)(22,35)(23,27)(24,30)(29,40)(31,41)(37,38);(10,12)(11,18)(13,24)(14,32)(15,25)(16,26)(17,33)(19,35)(20,38)(21,23)(22,36)(27,39)(28,30)(29,41)(31,40)(34,37)

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, 924);