C₉×#2231 #11766952

order	1152
nilpotency class	4
isoclinism	isoclinic class of #2230
automorphism	?
homology	Abelianization (H₁) = C₂³×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₉×#2231

Subgroups

	subgroup	G/H
center	C₂×C₉	#476
commutator	C₂×C₈	C₂³×C₉
Frattini, cosocle	C₂×C₃×C₈	C₂³×C₃
socle	C₂×C₃	C₃×#476
prime radical	C₃×#135	C₂²×C₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₉ ◁ C₂×C₄×C₉ ◁ C₄×C₈×C₉ ◁ G

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

normal subgroups only

This group has 180 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)(10,11,16,21)(12,22,25,20)(13,26)(14,30,23,19)(15,17,32,34)(18,35)(24,38)(27,40)(28,39)(29,33)(31,36)(37,41);(10,12,23,32,16,25,14,15)(11,17,30,20,21,34,19,22)(13,24,28,41,29,35,27,31)(18,33,37,39,38,26,36,40);(10,13)(11,18)(12,24)(14,27)(15,31)(16,29)(17,33)(19,36)(20,39)(21,38)(22,40)(23,28)(25,35)(26,34)(30,37)(32,41)

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, 963);