Finite Group Databasebeta

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C5×C17⋊(D13⋊C9) #34091035

order19890
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C17⋊(D13⋊C9)
unambiguous semidirect productC17⋊(C5×D13⋊C9)
unambiguous semidirect product(C13⋊C9)⋊(C5×D17)
unambiguous semidirect productD221⋊(C5×C9)
unambiguous semidirect product(C5×D221)⋊C9

Splittings

derived, HallC13×C17 ⋊ C2×C5×C9
HallC5×C17×C13⋊C9 ⋊ C2
HallC5×D221 ⋊ C9
HallC17×C13⋊C9 ⋊ C2×C5
HallC5×C13×C17 ⋊ C2×C9
HallC5×C13⋊C9 ⋊ D17
HallD221 ⋊ C5×C9
HallC13⋊C9 ⋊ C5×D17
HallC5×C17 ⋊ D13⋊C9
HallC5×C13 ⋊ C9×D17
SylowC17 ⋊ C5×D13⋊C9
SylowC13 ⋊ C5×C9×D17

Subgroups

subgroupG/H
center, hypercenterC3×C5C17⋊(D13⋊C3)
commutator, hypocenterC13×C17C2×C5×C9
FrattiniC3C5×C17⋊(D13⋊C3)
Fitting, socleC3×C5×C13×C17C2×C3
prime radicalC3×C5×D221C3
cosocleC3×C13×C17C2×C3×C5
LCSG ▷ C13×C17
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9945

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 20);