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D13⋊C3×D29⋊C7 #44539772

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

Aliases

direct productD13⋊C3×D29⋊C7
unambiguous semidirect productD13⋊(C3×D29⋊C7)
unambiguous semidirect productD29⋊(C7×D13⋊C3)
unambiguous semidirect product(D29×D13⋊C3)⋊C7
unambiguous semidirect product(D13×D29⋊C7)⋊C3
unambiguous semidirect product(C13⋊C3×D29⋊C7)⋊C2
unambiguous semidirect product(D13⋊C3×C29⋊C7)⋊C2
unambiguous semidirect product((C13⋊C3)⋊(D29⋊C7))⋊C2

Splittings

Fitting, socle, derived, HallC13×C29 ⋊ C22×C3×C7
HallD13×D29⋊C7 ⋊ C3
HallC13⋊C3×C29⋊C7 ⋊ C22
HallD29×D13⋊C3 ⋊ C7
HallC13×C29⋊C7 ⋊ C22×C3
HallD13×D29 ⋊ C3×C7
HallC29×C13⋊C3 ⋊ C22×C7
HallC29⋊C7 ⋊ C2×D13⋊C3
HallC13⋊C3 ⋊ C2×D29⋊C7
SylowC29 ⋊ C2×C7×D13⋊C3
SylowC13 ⋊ C2×C3×D29⋊C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC13×C29C22×C3×C7
LCSG ▷ C13×C29
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 377

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 67);