Finite Group Databasebeta

← Prev (#44539774) Next (#44539776) →

C2×D13⋊C3×C29⋊C7 #44539775

order31668
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×D13⋊C3×C29⋊C7
unambiguous semidirect productD13⋊(C2×C3×C29⋊C7)
unambiguous semidirect product(C13⋊C3)⋊(C22×C29⋊C7)
unambiguous semidirect product(C2×D13)⋊(C3×C29⋊C7)
unambiguous semidirect product(C2×C13⋊C3)⋊(C2×C29⋊C7)
unambiguous semidirect product(C2×C29×D13⋊C3)⋊C7
unambiguous semidirect product(C2×D13×C29⋊C7)⋊C3

Splittings

Fitting, socleC2×C13×C29 ⋊ C2×C3×C7
derived, HallC13×C29 ⋊ C22×C3×C7
HallC2×D13×C29⋊C7 ⋊ C3
HallC13⋊C3×C29⋊C7 ⋊ C22
HallC2×C29×D13⋊C3 ⋊ C7
HallC13×C29⋊C7 ⋊ C22×C3
HallC2×D13×C29 ⋊ C3×C7
HallC29×C13⋊C3 ⋊ C22×C7
HallC2×D13 ⋊ C3×C29⋊C7
HallC13⋊C3 ⋊ C22×C29⋊C7
SylowC29 ⋊ C2×C7×D13⋊C3
SylowC13 ⋊ C22×C3×C29⋊C7

Subgroups

subgroupG/H
center, hypercenterC2D13⋊C3×C29⋊C7
commutator, cosocle, hypocenterC13×C29C22×C3×C7
FrattiniC1G
Fitting, socleC2×C13×C29C2×C3×C7
LCSG ▷ C13×C29
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 754

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 70);