Finite Group Databasebeta

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C32×C17×C29⋊C7 #44526918

order31059
automorphism?
homologyAbelianization (H1) = C32×C7×C17 · Schur multiplier (H2) = C3

Aliases

direct productC32×C17×C29⋊C7
unambiguous semidirect productC29⋊(C32×C7×C17)
unambiguous semidirect product(C3×C29)⋊(C3×C7×C17)
unambiguous semidirect product(C32×C29)⋊(C7×C17)
unambiguous semidirect product(C17×C29)⋊(C32×C7)
unambiguous semidirect product(C3×C17×C29)⋊(C3×C7)
unambiguous semidirect product(C32×C17×C29)⋊C7

Splittings

Fitting, socle, HallC32×C17×C29 ⋊ C7
derived, SylowC29 ⋊ C32×C7×C17
HallC17×C29 ⋊ C32×C7
HallC32×C29 ⋊ C7×C17

Subgroups

subgroupG/H
center, hypercenterC32×C17C29⋊C7
commutator, cosocle, hypocenterC29C32×C7×C17
FrattiniC1G
Fitting, socleC32×C17×C29C7
LCSG ▷ C29
UCSC1 ◁ C32×C17

48 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, 5);