Finite Group Databasebeta

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C17×D1015 #46828514

order34510
automorphism?
homologyAbelianization (H1) = C2×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×D1015
unambiguous semidirect productC5⋊(C17×D203)
unambiguous semidirect productC7⋊(C17×D145)
unambiguous semidirect productC29⋊(C17×D35)

Splittings

Fitting, socle, HallC5×C7×C17×C29 ⋊ C2
derived, HallC5×C7×C29 ⋊ C2×C17
HallC7×C17×C29 ⋊ D5
HallC5×C17×C29 ⋊ D7
HallC5×C7×C17 ⋊ D29
HallC17×C29 ⋊ D35
HallC7×C29 ⋊ D5×C17
HallC5×C29 ⋊ D7×C17
HallC7×C17 ⋊ D145
HallC5×C17 ⋊ D203
HallC5×C7 ⋊ C17×D29
SylowC29 ⋊ C17×D35
SylowC7 ⋊ C17×D145
SylowC5 ⋊ C17×D203

Subgroups

subgroupG/H
center, hypercenterC17D1015
commutator, cosocle, hypocenterC5×C7×C29C2×C17
FrattiniC1G
Fitting, socleC5×C7×C17×C29C2
LCSG ▷ C5×C7×C29
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17255

Conjugacy classes & character table

8653 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34510, 15);