Finite Group Databasebeta

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C2×C5×C9×C17×D11 #46777951

order33660
automorphism?
homologyAbelianization (H1) = C22×C5×C9×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C9×C17×D11

Splittings

FittingC2×C5×C9×C11×C17 ⋊ C2
derived, SylowC11 ⋊ C22×C5×C9×C17
HallC5×C9×C11×C17 ⋊ C22
HallC9×C11×C17 ⋊ C22×C5
HallC5×C11×C17 ⋊ C22×C9
HallC5×C9×C11 ⋊ C22×C17
HallC11×C17 ⋊ C22×C5×C9
HallC9×C11 ⋊ C22×C5×C17
HallC5×C11 ⋊ C22×C9×C17

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9×C17D11
commutator, hypocenterC11C22×C5×C9×C17
FrattiniC3C2×C3×C5×C17×D11
FittingC2×C5×C9×C11×C17C2
socleC2×C3×C5×C11×C17C2×C3
prime radicalC2×C3×C5×C17×D11C3
cosocleC3×C11C22×C3×C5×C17
LCSG ▷ C11
UCSC1 ◁ C2×C5×C9×C17

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16830

Conjugacy classes & character table

10710 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 119);