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C3×(C31⋊C9)⋊C9 #21419290

order7533
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C33

Aliases

direct productC3×(C31⋊C9)⋊C9

Splittings

SylowC31 ⋊ C3×C9⋊C9

Subgroups

subgroupG/H
centerC33C3×C31⋊C3
commutatorC3×C31C32×C9
FrattiniC32C32×C31⋊C3
FittingC32×C9×C31C3
socleC33×C31C32
hypercenterC32×C9C31⋊C3
hypocenterC31C3×C9⋊C9
LCSG ▷ C3×C31 ▷ C31
UCSC1 ◁ C33 ◁ C32×C9

180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

909 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#36379842, C9×(C31⋊C9)⋊C9, #36379850, …
maximal normal subgroup of#36379842, C9×(C31⋊C9)⋊C9, #36379850, …
maximal quotient ofC3×C31⋊#6855, C9×(C31⋊C9)⋊C9, #36379850, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7533, 160);