Finite Group Databasebeta

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C13×(C43⋊C7)⋊C9 #47976237

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

Aliases

direct productC13×(C43⋊C7)⋊C9
unambiguous semidirect product(C43⋊C7)⋊(C9×C13)
unambiguous semidirect product(C43⋊C9)⋊(C7×C13)
unambiguous semidirect product(C13×C43⋊C9)⋊C7

Splittings

derived, SylowC43 ⋊ C7×C9×C13
HallC13×C43⋊C9 ⋊ C7
HallC13×C43⋊C7 ⋊ C9
HallC13×C43 ⋊ C7×C9
HallC43⋊C9 ⋊ C7×C13
HallC43⋊C7 ⋊ C9×C13

Subgroups

subgroupG/H
center, hypercenterC3×C13(C43⋊C3)⋊C7
commutator, hypocenterC43C7×C9×C13
FrattiniC3C13×(C43⋊C3)⋊C7
Fitting, socleC3×C13×C43C3×C7
prime radicalC3×C13×C43⋊C7C3
cosocleC3×C43C3×C7×C13
LCSG ▷ C43
UCSC1 ◁ C3×C13

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5031

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35217, 16);