Finite Group Databasebeta

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C17×D1045 #48001050

order35530
automorphism?
homologyAbelianization (H1) = C2×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×D1045
unambiguous semidirect productC5⋊(C17×D209)
unambiguous semidirect productC11⋊(C17×D95)
unambiguous semidirect productC19⋊(C17×D55)

Splittings

Fitting, socle, HallC5×C11×C17×C19 ⋊ C2
derived, HallC5×C11×C19 ⋊ C2×C17
HallC11×C17×C19 ⋊ D5
HallC5×C17×C19 ⋊ D11
HallC5×C11×C17 ⋊ D19
HallC17×C19 ⋊ D55
HallC11×C19 ⋊ D5×C17
HallC11×C17 ⋊ D95
HallC5×C19 ⋊ C17×D11
HallC5×C17 ⋊ D209
HallC5×C11 ⋊ C17×D19
SylowC19 ⋊ C17×D55
SylowC11 ⋊ C17×D95
SylowC5 ⋊ C17×D209

Subgroups

subgroupG/H
center, hypercenterC17D1045
commutator, cosocle, hypocenterC5×C11×C19C2×C17
FrattiniC1G
Fitting, socleC5×C11×C17×C19C2
LCSG ▷ C5×C11×C19
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17765

Conjugacy classes & character table

8908 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35530, 15);