Finite Group Databasebeta

C17×C29×C7⋊C9 #44526916

order31059
automorphism?
homologyAbelianization (H1) = C9×C17×C29 · Schur multiplier (H2) = C1

Aliases

direct productC17×C29×C7⋊C9
unambiguous semidirect productC7⋊(C9×C17×C29)
unambiguous semidirect product(C7×C17)⋊(C9×C29)
unambiguous semidirect product(C7×C29)⋊(C9×C17)
unambiguous semidirect product(C7×C17×C29)⋊C9

Splittings

derived, SylowC7 ⋊ C9×C17×C29
HallC7×C17×C29 ⋊ C9
HallC7×C29 ⋊ C9×C17
HallC7×C17 ⋊ C9×C29

Subgroups

subgroupG/H
center, hypercenterC3×C17×C29ΓL(1,𝔽8)
commutator, hypocenterC7C9×C17×C29
FrattiniC3C17×ΓL(1,𝔽8)×C29
Fitting, socle, prime radicalC3×C7×C17×C29C3
cosocleC3×C7C3×C17×C29
LCSG ▷ C7
UCSC1 ◁ C3×C17×C29

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31059

Conjugacy classes & character table

7395 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31059, 3);