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C2×C3×C5×C181⋊C3 #30654348

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

Aliases

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

Splittings

Fitting, socleC2×C3×C5×C181 ⋊ C3
derived, SylowC181 ⋊ C2×C32×C5
HallC2×C5×C181 ⋊ C32
HallC5×C181 ⋊ C2×C32
HallC2×C181 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5C181⋊C3
commutator, cosocle, hypocenterC181C2×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C181C3
LCSG ▷ C181
UCSC1 ◁ C2×C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1890 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×Dic181⋊C3, C3×Dic905⋊C3, C3×Dic5×C181⋊C3, …
maximal normal subgroup ofC3×C5×Dic181⋊C3, C3×Dic905⋊C3, C3×Dic5×C181⋊C3, …
maximal quotient ofC3×C4×C5×C181⋊C3, C22×C3×C5×C181⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16290, 43);