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C2×C5⋊(D97⋊C9) #31775486

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

Aliases

direct productC2×C5⋊(D97⋊C9)
unambiguous semidirect product(C2×C5)⋊(D97⋊C9)
unambiguous semidirect product(C2×C97⋊C9)⋊D5
unambiguous semidirect product(C2×D485)⋊C9

Splittings

derived, HallC5×C97 ⋊ C22×C9
HallC5×C97⋊C9 ⋊ C22
HallC2×D485 ⋊ C9
HallC97⋊C9 ⋊ C2×D5
SylowC97 ⋊ C2×C9×D5
SylowC5 ⋊ C2×D97⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊(D97⋊C3)
commutator, hypocenterC5×C97C22×C9
FrattiniC3C2×C5⋊(D97⋊C3)
Fitting, socleC2×C3×C5×C97C2×C3
prime radicalC2×C3×D485C3
cosocleC3×C5×C97C22×C3
LCSG ▷ C5×C97
UCSC1 ◁ C2×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8730

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17460, 22);