Finite Group Databasebeta

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C5×C7×C11×C31⋊C3 #49088976

order35805
automorphism?
homologyAbelianization (H1) = C3×C5×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×C11×C31⋊C3
unambiguous semidirect product(C5×C31)⋊(C3×C7×C11)
unambiguous semidirect product(C5×C11×C31)⋊(C3×C7)

Splittings

Fitting, socle, HallC5×C7×C11×C31 ⋊ C3
derived, SylowC31 ⋊ C3×C5×C7×C11
HallC7×C11×C31 ⋊ C3×C5
HallC5×C11×C31 ⋊ C3×C7
HallC5×C7×C31 ⋊ C3×C11
HallC11×C31 ⋊ C3×C5×C7
HallC7×C31 ⋊ C3×C5×C11
HallC5×C31 ⋊ C3×C7×C11

Subgroups

subgroupG/H
center, hypercenterC5×C7×C11C31⋊C3
commutator, cosocle, hypocenterC31C3×C5×C7×C11
FrattiniC1G
Fitting, socleC5×C7×C11×C31C3
LCSG ▷ C31
UCSC1 ◁ C5×C7×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11935

Conjugacy classes & character table

5005 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35805, 8);