Finite Group Databasebeta

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C3×C31×D165 #44501880

order30690
automorphism?
homologyAbelianization (H1) = C2×C3×C31 · Schur multiplier (H2) = C1

Aliases

direct productC3×C31×D165
unambiguous semidirect productC3⋊(C3×C31×D55)
unambiguous semidirect productC5⋊(C3×C31×D33)
unambiguous semidirect productC11⋊(C3×D15×C31)

Splittings

Fitting, socle, HallC32×C5×C11×C31 ⋊ C2
derivedC3×C5×C11 ⋊ C2×C3×C31
HallC32×C11×C31 ⋊ D5
HallC5×C11×C31 ⋊ C3×D3
HallC32×C5×C31 ⋊ D11
HallC32×C5×C11 ⋊ C2×C31
HallC11×C31 ⋊ C3×D15
HallC32×C31 ⋊ D55
HallC5×C31 ⋊ C3×D33
HallC32×C11 ⋊ D5×C31
HallC5×C11 ⋊ C3×D3×C31
HallC32×C5 ⋊ D11×C31
SylowC11 ⋊ C3×D15×C31
SylowC32 ⋊ C31×D55
SylowC5 ⋊ C3×C31×D33

Subgroups

subgroupG/H
center, hypercenterC3×C31D165
commutator, cosocle, hypocenterC3×C5×C11C2×C3×C31
FrattiniC1G
Fitting, socleC32×C5×C11×C31C2
LCSG ▷ C3×C5×C11
UCSC1 ◁ C3×C31

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10230

Conjugacy classes & character table

7812 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 247);