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C17×D1085 #49146267

order36890
automorphism?
homologyAbelianization (H1) = C2×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×D1085
unambiguous semidirect productC5⋊(C17×D217)
unambiguous semidirect productC7⋊(C17×D155)
unambiguous semidirect productC31⋊(C17×D35)

Splittings

Fitting, socle, HallC5×C7×C17×C31 ⋊ C2
derived, HallC5×C7×C31 ⋊ C2×C17
HallC7×C17×C31 ⋊ D5
HallC5×C17×C31 ⋊ D7
HallC5×C7×C17 ⋊ D31
HallC17×C31 ⋊ D35
HallC7×C31 ⋊ D5×C17
HallC5×C31 ⋊ D7×C17
HallC7×C17 ⋊ D155
HallC5×C17 ⋊ D217
HallC5×C7 ⋊ C17×D31
SylowC31 ⋊ C17×D35
SylowC7 ⋊ C17×D155
SylowC5 ⋊ C17×D217

Subgroups

subgroupG/H
center, hypercenterC17D1085
commutator, cosocle, hypocenterC5×C7×C31C2×C17
FrattiniC1G
Fitting, socleC5×C7×C17×C31C2
LCSG ▷ C5×C7×C31
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18445

Conjugacy classes & character table

9248 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36890, 15);