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C2×C3×(C181⋊C3)⋊C5 #30654333

order16290
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×(C181⋊C3)⋊C5
unambiguous semidirect product(C2×C181⋊C3)⋊(C3×C5)
unambiguous semidirect product(C2×C181⋊C5)⋊C32
unambiguous semidirect product(C2×C3×C181⋊C3)⋊C5
unambiguous semidirect product(C2×C3×C181⋊C5)⋊C3

Splittings

Fitting, socleC2×C3×C181 ⋊ C3×C5
derived, SylowC181 ⋊ C2×C32×C5
HallC2×C3×C181⋊C3 ⋊ C5
HallC2×C181⋊C5 ⋊ C32
HallC3×C181⋊C3 ⋊ C2×C5
HallC181⋊C5 ⋊ C2×C32
HallC2×C181 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3(C181⋊C3)⋊C5
commutator, cosocle, hypocenterC181C2×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C181C3×C5
LCSG ▷ C181
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

162 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×(Dic181⋊C3)⋊C5, C3⋊((Dic181⋊C3)⋊C5), Dic3×(C181⋊C3)⋊C5, …
maximal normal subgroup ofC3×(Dic181⋊C3)⋊C5, C3⋊((Dic181⋊C3)⋊C5), Dic3×(C181⋊C3)⋊C5, …
maximal quotient ofC3×C4×(C181⋊C3)⋊C5, C22×C3×(C181⋊C3)⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16290, 28);