Finite Group Databasebeta

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C2×C32×C17×D55 #46778199

order33660
automorphism?
homologyAbelianization (H1) = C22×C32×C17 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×C17×D55
unambiguous semidirect product(C2×C5)⋊(C32×C17×D11)
unambiguous semidirect product(C2×C11)⋊(C32×D5×C17)

Splittings

Fitting, socleC2×C32×C5×C11×C17 ⋊ C2
derived, HallC5×C11 ⋊ C22×C32×C17
HallC32×C5×C11×C17 ⋊ C22
HallC32×C11×C17 ⋊ C2×D5
HallC5×C11×C17 ⋊ C22×C32
HallC32×C5×C17 ⋊ C2×D11
HallC32×C5×C11 ⋊ C22×C17
HallC11×C17 ⋊ C2×C32×D5
HallC32×C11 ⋊ C2×D5×C17
HallC5×C17 ⋊ C2×C32×D11
HallC32×C5 ⋊ C2×C17×D11
SylowC11 ⋊ C2×C32×D5×C17
SylowC5 ⋊ C2×C32×C17×D11

Subgroups

subgroupG/H
center, hypercenterC2×C32×C17D55
commutator, cosocle, hypocenterC5×C11C22×C32×C17
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C17C2
LCSG ▷ C5×C11
UCSC1 ◁ C2×C32×C17

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16830

Conjugacy classes & character table

8874 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 367);