Finite Group Databasebeta

← Prev (#44501854) Next (#44501856) →

C5×D33×C31⋊C3 #44501855

order30690
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D33×C31⋊C3
unambiguous semidirect productC3⋊(C5×D11×C31⋊C3)
unambiguous semidirect product(C5×C31×D33)⋊C3

Splittings

Fitting, socleC3×C5×C11×C31 ⋊ C2×C3
derivedC3×C11×C31 ⋊ C2×C3×C5
HallC3×C5×C11×C31⋊C3 ⋊ C2
HallC3×C11×C31⋊C3 ⋊ C2×C5
HallC5×C11×C31 ⋊ C3×D3
HallC3×C5×C31⋊C3 ⋊ D11
HallC11×C31 ⋊ C3×C5×D3
HallC3×C31⋊C3 ⋊ C5×D11
HallC5×C31 ⋊ C3×D33
HallC5×C11 ⋊ D3×C31⋊C3
SylowC31 ⋊ C3×C5×D33
SylowC11 ⋊ C5×D3×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC5D33×C31⋊C3
commutator, cosocle, hypocenterC3×C11×C31C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C31C2×C3
LCSG ▷ C3×C11×C31
UCSC1 ◁ C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5115

Conjugacy classes & character table

1170 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 222);