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C2×C17×D315 #36339283

order21420
automorphism?
homologyAbelianization (H1) = C22×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C17×D315
unambiguous semidirect product(C2×C5)⋊(C17×D63)
unambiguous semidirect product(C2×C7)⋊(C17×D45)
unambiguous semidirect product(C2×C9)⋊(C17×D35)

Splittings

FittingC2×C5×C7×C9×C17 ⋊ C2
derived, HallC5×C7×C9 ⋊ C22×C17
HallC5×C7×C9×C17 ⋊ C22
HallC7×C9×C17 ⋊ C2×D5
HallC5×C9×C17 ⋊ C2×D7
HallC5×C7×C17 ⋊ C2×D9
HallC9×C17 ⋊ C2×D35
HallC7×C17 ⋊ C2×D45
HallC5×C17 ⋊ C2×D63
HallC7×C9 ⋊ C2×D5×C17
HallC5×C9 ⋊ C2×D7×C17
HallC5×C7 ⋊ C2×C17×D9
SylowC9 ⋊ C2×C17×D35
SylowC7 ⋊ C2×C17×D45
SylowC5 ⋊ C2×C17×D63

Subgroups

subgroupG/H
center, hypercenterC2×C17D315
commutator, cosocle, hypocenterC5×C7×C9C22×C17
FrattiniC3C2×C17×D105
FittingC2×C5×C7×C9×C17C2
socleC2×C3×C5×C7×C17D3
LCSG ▷ C5×C7×C9
UCSC1 ◁ C2×C17

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10710

Conjugacy classes & character table

5406 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 115);