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C9×(C71⋊C5)⋊C7 #36375357

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

Aliases

direct productC9×(C71⋊C5)⋊C7
unambiguous semidirect product(C71⋊C5)⋊(C7×C9)
unambiguous semidirect product(C71⋊C7)⋊(C5×C9)
unambiguous semidirect product(C9×C71⋊C5)⋊C7
unambiguous semidirect product(C9×C71⋊C7)⋊C5

Splittings

Fitting, HallC9×C71 ⋊ C5×C7
derived, SylowC71 ⋊ C5×C7×C9
HallC9×C71⋊C7 ⋊ C5
HallC9×C71⋊C5 ⋊ C7
HallC71⋊C7 ⋊ C5×C9
HallC71⋊C5 ⋊ C7×C9

Subgroups

subgroupG/H
center, hypercenterC9(C71⋊C5)⋊C7
commutator, hypocenterC71C5×C7×C9
FrattiniC3C3×(C71⋊C5)⋊C7
FittingC9×C71C5×C7
socle, cosocleC3×C71C3×C5×C7
prime radicalC3×(C71⋊C5)⋊C7C3
LCSG ▷ C71
UCSC1 ◁ C9

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 639

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22365, 4);