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C9×#2956 #11767677

order1152
nilpotency class3
isoclinismisoclinic class of #576
automorphism?
homologyAbelianization (H1) = C23×C4×C9 · Schur multiplier (H2) = C25

Aliases

direct productC9×#2956

Subgroups

subgroupG/H
centerC4×C9C22×D4
commutatorC4C23×C4×C9
Frattini, cosocleC2×C3×C4C24×C3
socleC2×C3C2×C3×C4×D4
prime radicalC3×#575C2×C3
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C9 ◁ C2×C9×M16 ◁ G

687 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 25 points:

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

Conjugacy classes & character table

396 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofD9×#2956, #72268966
maximal subgroup ofD9×#2956, C9×#61110, #72268966
maximal normal subgroup ofD9×#2956, C9×#61110, #72268966

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 1688);