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C17×D315 #24924201

order10710
automorphism?
homologyAbelianization (H1) = C2×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×D315
unambiguous semidirect productC5⋊(C17×D63)
unambiguous semidirect productC7⋊(C17×D45)
unambiguous semidirect productC9⋊(C17×D35)

Splittings

Fitting, HallC5×C7×C9×C17 ⋊ C2
derived, HallC5×C7×C9 ⋊ C2×C17
HallC7×C9×C17 ⋊ D5
HallC5×C9×C17 ⋊ D7
HallC5×C7×C17 ⋊ D9
HallC9×C17 ⋊ D35
HallC7×C17 ⋊ D45
HallC5×C17 ⋊ D63
HallC7×C9 ⋊ D5×C17
HallC5×C9 ⋊ D7×C17
HallC5×C7 ⋊ C17×D9
SylowC9 ⋊ C17×D35
SylowC7 ⋊ C17×D45
SylowC5 ⋊ C17×D63

Subgroups

subgroupG/H
center, hypercenterC17D315
commutator, cosocle, hypocenterC5×C7×C9C2×C17
FrattiniC3C17×D105
FittingC5×C7×C9×C17C2
socleC3×C5×C7×C17D3
LCSG ▷ C5×C7×C9
UCSC1 ◁ C17

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2703 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD17×D315, D7×C17×D45, D119⋊D45, …
maximal normal subgroup ofD17×D315, D7×C17×D45, D119⋊D45, …
maximal quotient ofC17×Dic315, C2×C17×D315

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 16);