Finite Group Databasebeta

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C3×D5×C11×C31⋊C3 #44501849

order30690
automorphism?
homologyAbelianization (H1) = C2×C32×C11 · Schur multiplier (H2) = C3

Aliases

direct productC3×D5×C11×C31⋊C3
unambiguous semidirect productC5⋊(C2×C3×C11×C31⋊C3)
unambiguous semidirect product(D5×C31)⋊(C32×C11)
unambiguous semidirect product(C3×D5×C31)⋊(C3×C11)
unambiguous semidirect product(D5×C11×C31)⋊C32
unambiguous semidirect product(C3×D5×C11×C31)⋊C3

Splittings

Fitting, socleC3×C5×C11×C31 ⋊ C2×C3
derived, HallC5×C31 ⋊ C2×C32×C11
HallC3×C5×C11×C31⋊C3 ⋊ C2
HallD5×C11×C31 ⋊ C32
HallC5×C11×C31 ⋊ C2×C32
HallC3×C5×C31⋊C3 ⋊ C2×C11
HallC11×C31 ⋊ C32×D5
HallD5×C31 ⋊ C32×C11
HallC5×C11 ⋊ C2×C3×C31⋊C3
SylowC31 ⋊ C32×D5×C11
SylowC5 ⋊ C2×C3×C11×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C11D5×C31⋊C3
commutator, cosocle, hypocenterC5×C31C2×C32×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C31C2×C3
LCSG ▷ C5×C31
UCSC1 ◁ C3×C11

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5115

Conjugacy classes & character table

1716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 216);