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D39×D29⋊C7 #44539791

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

Aliases

direct productD39×D29⋊C7
unambiguous semidirect productD29⋊(C7×D39)
unambiguous semidirect product(C3×D29⋊C7)⋊D13
unambiguous semidirect product(D29×D39)⋊C7
unambiguous semidirect product(C13×D29⋊C7)⋊D3

Splittings

Fitting, socle, derived, HallC3×C13×C29 ⋊ C22×C7
HallC3×C13×C29⋊C7 ⋊ C22
HallD29×D39 ⋊ C7
HallC13×C29⋊C7 ⋊ C2×D3
HallC3×C29⋊C7 ⋊ C2×D13
HallC13×C29 ⋊ C2×D3×C7
HallC29⋊C7 ⋊ C2×D39
HallC3×C29 ⋊ C2×C7×D13
HallC3×C13 ⋊ C2×D29⋊C7
SylowC29 ⋊ C2×C7×D39
SylowC13 ⋊ D3×D29⋊C7
SylowC3 ⋊ D13×D29⋊C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C13×C29C22×C7
LCSG ▷ C3×C13×C29
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1131

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 86);