Finite Group Databasebeta

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C9×#2008 #11766729

order1152
nilpotency class3
isoclinismisoclinic class of #2008
automorphism?
homologyAbelianization (H1) = C23×C9 · Schur multiplier (H2) = C24

Aliases

direct productC9×#2008

Subgroups

subgroupG/H
centerC2×C9#392
commutatorC22×C4C23×C9
Frattini, cosocleC22×C3×C4C23×C3
socleC2×C3C3×#392
prime radicalC3×#2008C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C9 ◁ C22×C4×C9 ◁ G

570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 25
transitive degreeμt(G) = 144

A minimal faithful permutation representation — 3 generators on 25 points:

(1,2,3,4,5,6,7,8,9)(10,11)(12,20)(13,18)(14,17)(15,19)(16,21)(22,25)(23,24);(10,12)(11,16)(13,23)(14,21)(15,22)(17,25)(18,20)(19,24);(11,17)(13,14)(16,20)(18,19)(21,23)(24,25)

Conjugacy classes & character table

207 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of#72269039
maximal subgroup of#72269039
maximal normal subgroup of#72269039

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 740);