Finite Group Databasebeta

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C9×#1094 #11757818

order972
isoclinismisoclinic class of C9⋊A4
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C2×C32

Aliases

direct productC9×#1094

Splittings

SylowC22 ⋊ C9×3−1+2

Subgroups

subgroupG/H
centerC3×C9C3×A4
commutatorC22×C3C32×C9
FrattiniC32C32×A4
FittingC22×C32×C9C3
socle, cosocleC22×C32C33
prime radicalC22×C33C32
hypercenterC32×C9A4
hypocenterC22C9×3−1+2
LCSG ▷ C22×C3 ▷ C22
UCSC1 ◁ C3×C9 ◁ C32×C9

198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 162

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×((C22⋊C9)⋊C2)⋊C3, #14518045, D9×#1094, …
maximal normal subgroup ofC9×((C22⋊C9)⋊C2)⋊C3, #14518045, D9×#1094, …
maximal quotient ofC9×#6204, C2×C9×#1094, C22⋊C9×#1094

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(972, 543);