Finite Group Databasebeta

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C5×C9×C71⋊C7 #36375355

order22365
automorphism?
homologyAbelianization (H1) = C5×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×C71⋊C7
unambiguous semidirect product(C5×C71)⋊(C7×C9)
unambiguous semidirect product(C5×C9×C71)⋊C7

Splittings

Fitting, HallC5×C9×C71 ⋊ C7
derived, SylowC71 ⋊ C5×C7×C9
HallC9×C71 ⋊ C5×C7
HallC5×C71 ⋊ C7×C9

Subgroups

subgroupG/H
center, hypercenterC5×C9C71⋊C7
commutator, hypocenterC71C5×C7×C9
FrattiniC3C3×C5×C71⋊C7
FittingC5×C9×C71C7
socleC3×C5×C71C3×C7
prime radicalC3×C5×C71⋊C7C3
cosocleC3×C71C3×C5×C7
LCSG ▷ C71
UCSC1 ◁ C5×C9

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3195

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22365, 2);