Finite Group Databasebeta

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C9×C13×C43⋊C7 #47976223

order35217
automorphism?
homologyAbelianization (H1) = C7×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC9×C13×C43⋊C7
unambiguous semidirect product(C9×C43)⋊(C7×C13)
unambiguous semidirect product(C9×C13×C43)⋊C7

Splittings

Fitting, HallC9×C13×C43 ⋊ C7
derived, SylowC43 ⋊ C7×C9×C13
HallC13×C43 ⋊ C7×C9
HallC9×C43 ⋊ C7×C13

Subgroups

subgroupG/H
center, hypercenterC9×C13C43⋊C7
commutator, hypocenterC43C7×C9×C13
FrattiniC3C3×C13×C43⋊C7
FittingC9×C13×C43C7
socleC3×C13×C43C3×C7
prime radicalC3×C13×C43⋊C7C3
cosocleC3×C43C3×C7×C13
LCSG ▷ C43
UCSC1 ◁ C9×C13

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5031

Conjugacy classes & character table

1521 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35217, 2);