Finite Group Databasebeta

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C2×C49×D165 #44568434

order32340
automorphism?
homologyAbelianization (H1) = C22×C49 · Schur multiplier (H2) = C2

Aliases

direct productC2×C49×D165
unambiguous semidirect product(C2×C3)⋊(C49×D55)
unambiguous semidirect product(C2×C5)⋊(C49×D33)
unambiguous semidirect product(C2×C11)⋊(D15×C49)

Splittings

FittingC2×C3×C5×C11×C49 ⋊ C2
derived, HallC3×C5×C11 ⋊ C22×C49
HallC3×C5×C11×C49 ⋊ C22
HallC5×C11×C49 ⋊ C2×D3
HallC3×C11×C49 ⋊ C2×D5
HallC3×C5×C49 ⋊ C2×D11
HallC11×C49 ⋊ C2×D15
HallC5×C49 ⋊ C2×D33
HallC3×C49 ⋊ C2×D55
HallC5×C11 ⋊ C2×D3×C49
HallC3×C11 ⋊ C2×D5×C49
HallC3×C5 ⋊ C2×D11×C49
SylowC11 ⋊ C2×D15×C49
SylowC5 ⋊ C2×C49×D33
SylowC3 ⋊ C2×C49×D55

Subgroups

subgroupG/H
center, hypercenterC2×C49D165
commutator, hypocenterC3×C5×C11C22×C49
FrattiniC7C2×C7×D165
FittingC2×C3×C5×C11×C49C2
socleC2×C3×C5×C7×C11C2×C7
prime radicalC2×C7×D165C7
cosocleC3×C5×C7×C11C22×C7
LCSG ▷ C3×C5×C11
UCSC1 ◁ C2×C49

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16170

Conjugacy classes & character table

8232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 136);