Finite Group Databasebeta

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C2×C17×D495 #46777939

order33660
automorphism?
homologyAbelianization (H1) = C22×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C17×D495
unambiguous semidirect product(C2×C5)⋊(C17×D99)
unambiguous semidirect product(C2×C9)⋊(C17×D55)
unambiguous semidirect product(C2×C11)⋊(C17×D45)

Splittings

FittingC2×C5×C9×C11×C17 ⋊ C2
derived, HallC5×C9×C11 ⋊ C22×C17
HallC5×C9×C11×C17 ⋊ C22
HallC9×C11×C17 ⋊ C2×D5
HallC5×C11×C17 ⋊ C2×D9
HallC5×C9×C17 ⋊ C2×D11
HallC11×C17 ⋊ C2×D45
HallC9×C17 ⋊ C2×D55
HallC9×C11 ⋊ C2×D5×C17
HallC5×C17 ⋊ C2×D99
HallC5×C11 ⋊ C2×C17×D9
HallC5×C9 ⋊ C2×C17×D11
SylowC11 ⋊ C2×C17×D45
SylowC9 ⋊ C2×C17×D55
SylowC5 ⋊ C2×C17×D99

Subgroups

subgroupG/H
center, hypercenterC2×C17D495
commutator, cosocle, hypocenterC5×C9×C11C22×C17
FrattiniC3C2×C17×D165
FittingC2×C5×C9×C11×C17C2
socleC2×C3×C5×C11×C17D3
LCSG ▷ C5×C9×C11
UCSC1 ◁ C2×C17

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16830

Conjugacy classes & character table

8466 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 107);