Finite Group Databasebeta

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C2×C5×D97⋊C9 #31775485

order17460
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D97⋊C9
unambiguous semidirect productD97⋊(C2×C5×C9)
unambiguous semidirect product(C2×D97)⋊(C5×C9)
unambiguous semidirect product(C97⋊C9)⋊(C22×C5)
unambiguous semidirect product(C2×C97⋊C9)⋊(C2×C5)
unambiguous semidirect product(C2×C5×D97)⋊C9

Splittings

derived, SylowC97 ⋊ C22×C5×C9
HallC5×C97⋊C9 ⋊ C22
HallC2×C5×D97 ⋊ C9
HallC97⋊C9 ⋊ C22×C5
HallC5×C97 ⋊ C22×C9
HallC2×D97 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D97⋊C3
commutator, hypocenterC97C22×C5×C9
FrattiniC3C2×C5×D97⋊C3
Fitting, socleC2×C3×C5×C97C2×C3
prime radicalC2×C3×C5×D97C3
cosocleC3×C97C22×C3×C5
LCSG ▷ C97
UCSC1 ◁ C2×C3×C5

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8730

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17460, 21);