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C2×C9⋊(D101⋊C5) #32911386

order18180
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9⋊(D101⋊C5)
unambiguous semidirect product(C2×C9)⋊(D101⋊C5)
unambiguous semidirect product(C2×C101⋊C5)⋊D9
unambiguous semidirect product(C2×D909)⋊C5

Splittings

FittingC2×C9×C101 ⋊ C2×C5
derived, HallC9×C101 ⋊ C22×C5
HallC9×C101⋊C5 ⋊ C22
HallC2×D909 ⋊ C5
HallC101⋊C5 ⋊ C2×D9
SylowC101 ⋊ C2×C5×D9
SylowC9 ⋊ C2×D101⋊C5

Subgroups

subgroupG/H
center, hypercenterC2C9⋊(D101⋊C5)
commutator, cosocle, hypocenterC9×C101C22×C5
FrattiniC3C2×C3⋊(D101⋊C5)
FittingC2×C9×C101C2×C5
socleC2×C3×C101C5×D3
LCSG ▷ C9×C101
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1818

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18180, 19);