Finite Group Databasebeta

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C31×C3⋊D165 #44501888

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

Aliases

direct productC31×C3⋊D165
unambiguous semidirect productC3⋊(C31×D165)
unambiguous semidirect productC5⋊(C31×C3⋊D33)
unambiguous semidirect productC11⋊(C31×C3⋊D15)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC31C3⋊D165
commutator, cosocle, hypocenterC32×C5×C11C2×C31
FrattiniC1G
Fitting, socleC32×C5×C11×C31C2
LCSG ▷ C32×C5×C11
UCSC1 ◁ C31

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15345

Conjugacy classes & character table

7719 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 255);