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C17×D585 #34091031

order19890
automorphism?
homologyAbelianization (H1) = C2×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×D585
unambiguous semidirect productC5⋊(C17×D117)
unambiguous semidirect productC9⋊(C17×D65)
unambiguous semidirect productC13⋊(C17×D45)

Splittings

Fitting, HallC5×C9×C13×C17 ⋊ C2
derived, HallC5×C9×C13 ⋊ C2×C17
HallC9×C13×C17 ⋊ D5
HallC5×C13×C17 ⋊ D9
HallC5×C9×C17 ⋊ D13
HallC13×C17 ⋊ D45
HallC9×C17 ⋊ D65
HallC9×C13 ⋊ D5×C17
HallC5×C17 ⋊ D117
HallC5×C13 ⋊ C17×D9
HallC5×C9 ⋊ C17×D13
SylowC13 ⋊ C17×D45
SylowC9 ⋊ C17×D65
SylowC5 ⋊ C17×D117

Subgroups

subgroupG/H
center, hypercenterC17D585
commutator, cosocle, hypocenterC5×C9×C13C2×C17
FrattiniC3C17×D195
FittingC5×C9×C13×C17C2
socleC3×C5×C13×C17D3
LCSG ▷ C5×C9×C13
UCSC1 ◁ C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9945

Conjugacy classes & character table

4998 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 16);