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C2×D181⋊C5 #16813733

order3620
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×D181⋊C5
unambiguous semidirect productD181⋊(C2×C5)
unambiguous semidirect product(C2×D181)⋊C5
unambiguous semidirect product(C181⋊C5)⋊C22
unambiguous semidirect product(C2×C181⋊C5)⋊C2

Splittings

Fitting, socleC2×C181 ⋊ C2×C5
derived, SylowC181 ⋊ C22×C5
HallC181⋊C5 ⋊ C22
HallC2×D181 ⋊ C5

Subgroups

subgroupG/H
center, hypercenterC2D181⋊C5
commutator, cosocle, hypocenterC181C22×C5
FrattiniC1G
Fitting, socleC2×C181C2×C5
LCSG ▷ C181
UCSC1 ◁ C2

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 362

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(D181⋊C3)⋊C5, D3×D181⋊C5, C2×C3×D181⋊C5, …
maximal normal subgroup ofC2×(D181⋊C3)⋊C5, C2×C3×D181⋊C5, C2×C5×D181⋊C5, …
maximal quotient ofD3×D181⋊C5, C2×C3×D181⋊C5, C2×C3⋊(D181⋊C5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3620, 9);