Finite Group Databasebeta

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C9×C11⋊C5×C71 #47975786

order35145
automorphism?
homologyAbelianization (H1) = C5×C9×C71 · Schur multiplier (H2) = C1

Aliases

direct productC9×C11⋊C5×C71
unambiguous semidirect productC11⋊(C5×C9×C71)
unambiguous semidirect product(C9×C11)⋊(C5×C71)

Splittings

Fitting, HallC9×C11×C71 ⋊ C5
derived, SylowC11 ⋊ C5×C9×C71
HallC11×C71 ⋊ C5×C9
HallC9×C11 ⋊ C5×C71

Subgroups

subgroupG/H
center, hypercenterC9×C71C11⋊C5
commutator, hypocenterC11C5×C9×C71
FrattiniC3C3×C11⋊C5×C71
FittingC9×C11×C71C5
socleC3×C11×C71C3×C5
prime radicalC3×C11⋊C5×C71C3
cosocleC3×C11C3×C5×C71
LCSG ▷ C11
UCSC1 ◁ C9×C71

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7029

Conjugacy classes & character table

4473 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35145, 3);