Finite Group Databasebeta

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C2×C9×D101⋊C5 #32911385

order18180
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×D101⋊C5
unambiguous semidirect productD101⋊(C2×C5×C9)
unambiguous semidirect product(C2×D101)⋊(C5×C9)
unambiguous semidirect product(C101⋊C5)⋊(C22×C9)
unambiguous semidirect product(C2×C101⋊C5)⋊(C2×C9)
unambiguous semidirect product(C2×C9×D101)⋊C5

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C9D101⋊C5
commutator, hypocenterC101C22×C5×C9
FrattiniC3C2×C3×D101⋊C5
FittingC2×C9×C101C2×C5
socleC2×C3×C101C2×C3×C5
prime radicalC2×C3×D101⋊C5C3
cosocleC3×C101C22×C3×C5
LCSG ▷ C101
UCSC1 ◁ C2×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1818

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18180, 18);