Finite Group Databasebeta

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C2×C13⋊C3×D29⋊C7 #44539776

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

Aliases

direct productC2×C13⋊C3×D29⋊C7
unambiguous semidirect productD29⋊(C2×C7×C13⋊C3)
unambiguous semidirect product(C2×D29)⋊(C7×C13⋊C3)
unambiguous semidirect product(C29⋊C7)⋊(C22×C13⋊C3)
unambiguous semidirect product(C2×C29⋊C7)⋊(C2×C13⋊C3)
unambiguous semidirect product(C2×C13⋊C3×D29)⋊C7
unambiguous semidirect product(C2×C13×D29⋊C7)⋊C3

Splittings

Fitting, socleC2×C13×C29 ⋊ C2×C3×C7
derived, HallC13×C29 ⋊ C22×C3×C7
HallC2×C13×D29⋊C7 ⋊ C3
HallC13⋊C3×C29⋊C7 ⋊ C22
HallC2×C13⋊C3×D29 ⋊ C7
HallC13×C29⋊C7 ⋊ C22×C3
HallC2×C13×D29 ⋊ C3×C7
HallC29×C13⋊C3 ⋊ C22×C7
HallC29⋊C7 ⋊ C22×C13⋊C3
HallC2×D29 ⋊ C7×C13⋊C3
SylowC29 ⋊ C22×C7×C13⋊C3
SylowC13 ⋊ C2×C3×D29⋊C7

Subgroups

subgroupG/H
center, hypercenterC2C13⋊C3×D29⋊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

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 71);