Finite Group Databasebeta

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C31⋊C3×D165 #44501859

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

Aliases

direct productC31⋊C3×D165
unambiguous semidirect productC3⋊(C31⋊C3×D55)
unambiguous semidirect productC5⋊(D33×C31⋊C3)
unambiguous semidirect productC11⋊(D15×C31⋊C3)
unambiguous semidirect product(C31×D165)⋊C3

Splittings

Fitting, socle, derivedC3×C5×C11×C31 ⋊ C2×C3
HallC3×C5×C11×C31⋊C3 ⋊ C2
HallC3×C11×C31⋊C3 ⋊ D5
HallC5×C11×C31 ⋊ C3×D3
HallC3×C5×C31⋊C3 ⋊ D11
HallC11×C31 ⋊ C3×D15
HallC3×C31⋊C3 ⋊ D55
HallC5×C31 ⋊ C3×D33
HallC5×C11 ⋊ D3×C31⋊C3
SylowC31 ⋊ C3×D165
SylowC11 ⋊ D15×C31⋊C3
SylowC5 ⋊ D33×C31⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C11×C31C2×C3
LCSG ▷ C3×C5×C11×C31
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5115

Conjugacy classes & character table

1092 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 226);