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C32×D181⋊C5 #30654334

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

Aliases

direct productC32×D181⋊C5
unambiguous semidirect product(C32×D181)⋊C5

Splittings

Fitting, socle, HallC32×C181 ⋊ C2×C5
derived, SylowC181 ⋊ C2×C32×C5
HallC32×C181⋊C5 ⋊ C2
HallC32×D181 ⋊ C5
HallC181⋊C5 ⋊ C2×C32
HallD181 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC32D181⋊C5
commutator, cosocle, hypocenterC181C2×C32×C5
FrattiniC1G
Fitting, socleC32×C181C2×C5
LCSG ▷ C181
UCSC1 ◁ C32

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC32×#10624382⋊C5, C3×C3⋊(#10624382⋊C5), C3×D3×D181⋊C5, …
maximal normal subgroup ofC32×#10624382⋊C5, C3×C3⋊(#10624382⋊C5), C3×D3×D181⋊C5, …
maximal quotient ofC32×Dic181⋊C5, C2×C32×D181⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16290, 29);