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C3×C3⋊(D181⋊C5) #30654335

order16290
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C3⋊(D181⋊C5)
unambiguous semidirect productC3⋊(C3×D181⋊C5)
unambiguous semidirect product(C3×D543)⋊C5

Splittings

Fitting, socle, HallC32×C181 ⋊ C2×C5
derivedC3×C181 ⋊ C2×C3×C5
HallC32×C181⋊C5 ⋊ C2
HallC3×D543 ⋊ C5
HallC181⋊C5 ⋊ C3×D3
SylowC181 ⋊ C3×C5×D3
SylowC32 ⋊ D181⋊C5

Subgroups

subgroupG/H
center, hypercenterC3C3⋊(D181⋊C5)
commutator, cosocle, hypocenterC3×C181C2×C3×C5
FrattiniC1G
Fitting, socleC32×C181C2×C5
LCSG ▷ C3×C181
UCSC1 ◁ C3

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

207 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D3×D181⋊C5, D3×C3⋊(D181⋊C5), (C3⋊D3)⋊(D181⋊C5), …
maximal normal subgroup ofC3×D3×D181⋊C5, D3×C3⋊(D181⋊C5), (C3⋊D3)⋊(D181⋊C5), …
maximal quotient ofC3×C3⋊(Dic181⋊C5), C2×C3×C3⋊(D181⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16290, 30);