Finite Group Databasebeta

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C3×C5⋊(C11⋊(D31⋊C3)) #44501850

order30690
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5⋊(C11⋊(D31⋊C3))
unambiguous semidirect productC5⋊(C3×C11⋊(D31⋊C3))
unambiguous semidirect productC11⋊(C3×C5⋊(D31⋊C3))
unambiguous semidirect product(C31⋊C3)⋊(C3×D55)
unambiguous semidirect productD1705⋊C32
unambiguous semidirect product(C3×D1705)⋊C3

Splittings

Fitting, socleC3×C5×C11×C31 ⋊ C2×C3
derived, HallC5×C11×C31 ⋊ C2×C32
HallC3×C5×C11×C31⋊C3 ⋊ C2
HallD1705 ⋊ C32
HallC3×C11×C31⋊C3 ⋊ D5
HallC3×C5×C31⋊C3 ⋊ D11
HallC11×C31 ⋊ C32×D5
HallC3×C31⋊C3 ⋊ D55
HallC5×C31 ⋊ C32×D11
HallC5×C11 ⋊ C3×D31⋊C3
SylowC31 ⋊ C32×D55
SylowC11 ⋊ C3×C5⋊(D31⋊C3)
SylowC5 ⋊ C3×C11⋊(D31⋊C3)

Subgroups

subgroupG/H
center, hypercenterC3C5⋊(C11⋊(D31⋊C3))
commutator, cosocle, hypocenterC5×C11×C31C2×C32
FrattiniC1G
Fitting, socleC3×C5×C11×C31C2×C3
LCSG ▷ C5×C11×C31
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5115

Conjugacy classes & character table

1086 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 217);