Finite Group Databasebeta

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C3×C5×C31×D33 #44501876

order30690
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C31 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC32×C5×C11×C31 ⋊ C2
derivedC3×C11 ⋊ C2×C3×C5×C31
HallC32×C11×C31 ⋊ C2×C5
HallC5×C11×C31 ⋊ C3×D3
HallC32×C5×C31 ⋊ D11
HallC32×C5×C11 ⋊ C2×C31
HallC11×C31 ⋊ C3×C5×D3
HallC32×C31 ⋊ C5×D11
HallC32×C11 ⋊ C2×C5×C31
HallC5×C11 ⋊ C3×D3×C31
HallC32×C5 ⋊ D11×C31
SylowC11 ⋊ C3×C5×D3×C31
SylowC32 ⋊ C5×D11×C31

Subgroups

subgroupG/H
center, hypercenterC3×C5×C31D33
commutator, cosocle, hypocenterC3×C11C2×C3×C5×C31
FrattiniC1G
Fitting, socleC32×C5×C11×C31C2
LCSG ▷ C3×C11
UCSC1 ◁ C3×C5×C31

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10230

Conjugacy classes & character table

8370 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 243);