Finite Group Databasebeta

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C2×C3×C5×C11×C31⋊C3 #44501866

order30690
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C11 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C5×C11×C31⋊C3
unambiguous semidirect product(C2×C5×C31)⋊(C32×C11)
unambiguous semidirect product(C2×C3×C5×C31)⋊(C3×C11)
unambiguous semidirect product(C2×C5×C11×C31)⋊C32
unambiguous semidirect product(C2×C3×C5×C11×C31)⋊C3

Splittings

Fitting, socleC2×C3×C5×C11×C31 ⋊ C3
derived, SylowC31 ⋊ C2×C32×C5×C11
HallC2×C5×C11×C31 ⋊ C32
HallC5×C11×C31 ⋊ C2×C32
HallC2×C11×C31 ⋊ C32×C5
HallC11×C31 ⋊ C2×C32×C5
HallC2×C5×C31 ⋊ C32×C11
HallC5×C31 ⋊ C2×C32×C11
HallC2×C31 ⋊ C32×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C11C31⋊C3
commutator, cosocle, hypocenterC31C2×C32×C5×C11
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C31C3
LCSG ▷ C31
UCSC1 ◁ C2×C3×C5×C11

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10230

Conjugacy classes & character table

4290 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 233);