Finite Group Databasebeta

C9×C17×C29⋊C7 #44526915

order31059
automorphism?
homologyAbelianization (H1) = C7×C9×C17 · Schur multiplier (H2) = C1

Aliases

direct productC9×C17×C29⋊C7
unambiguous semidirect productC29⋊(C7×C9×C17)
unambiguous semidirect product(C9×C29)⋊(C7×C17)
unambiguous semidirect product(C17×C29)⋊(C7×C9)
unambiguous semidirect product(C9×C17×C29)⋊C7

Splittings

Fitting, HallC9×C17×C29 ⋊ C7
derived, SylowC29 ⋊ C7×C9×C17
HallC17×C29 ⋊ C7×C9
HallC9×C29 ⋊ C7×C17

Subgroups

subgroupG/H
center, hypercenterC9×C17C29⋊C7
commutator, hypocenterC29C7×C9×C17
FrattiniC3C3×C17×C29⋊C7
FittingC9×C17×C29C7
socleC3×C17×C29C3×C7
prime radicalC3×C17×C29⋊C7C3
cosocleC3×C29C3×C7×C17
LCSG ▷ C29
UCSC1 ◁ C9×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4437

Conjugacy classes & character table

1683 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31059, 2);