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C7×C9×C71⋊C5 #36375356

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

Aliases

direct productC7×C9×C71⋊C5
unambiguous semidirect product(C7×C9×C71)⋊C5

Splittings

Fitting, HallC7×C9×C71 ⋊ C5
derived, SylowC71 ⋊ C5×C7×C9
HallC9×C71 ⋊ C5×C7
HallC7×C71 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC7×C9C71⋊C5
commutator, hypocenterC71C5×C7×C9
FrattiniC3C3×C7×C71⋊C5
FittingC7×C9×C71C5
socleC3×C7×C71C3×C5
prime radicalC3×C7×C71⋊C5C3
cosocleC3×C71C3×C5×C7
LCSG ▷ C71
UCSC1 ◁ C7×C9

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4473

Conjugacy classes & character table

1197 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22365, 3);