C₉×#2191 #11766912

order	1152
nilpotency class	4
isoclinism	isoclinic class of #2190
automorphism	?
homology	Abelianization (H₁) = C₂³×C₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₉×#2191

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×#575	C₂×C₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₉ ◁ C₂×C₄×C₉ ◁ C₂×C₉×M₁₆ ◁ G

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

normal subgroups only

This group has 324 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)(10,11,15,19)(12,20,22,38)(13,24,26,40)(14,29,27,18)(16,31,32,21)(17,34,36,28)(23,39,30,35)(25,37,41,33);(10,12)(11,16)(13,25)(14,30)(15,22)(17,35)(18,37)(19,32)(20,24)(21,28)(23,27)(26,41)(29,33)(31,34)(36,39)(38,40);(13,26)(17,36)(20,38)(21,31)(24,40)(25,41)(28,34)(35,39)

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 923);