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D29×C5⋊(D13⋊C3) #36383124

order22620
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD29×C5⋊(D13⋊C3)
unambiguous semidirect product(C5×D29)⋊(D13⋊C3)
unambiguous semidirect product(C13⋊C3×D29)⋊D5
unambiguous semidirect product(D29×D65)⋊C3

Splittings

Fitting, socle, derived, HallC5×C13×C29 ⋊ C22×C3
HallD29×D65 ⋊ C3
HallC5×C29×C13⋊C3 ⋊ C22
HallC29×C13⋊C3 ⋊ C2×D5
HallC13×C29 ⋊ C2×C3×D5
HallC5×C13⋊C3 ⋊ C2×D29
HallC5×C29 ⋊ C2×D13⋊C3
HallC5×C13 ⋊ C2×C3×D29
HallC13⋊C3 ⋊ D5×D29
SylowC29 ⋊ C2×C5⋊(D13⋊C3)
SylowC13 ⋊ C3×D5×D29
SylowC5 ⋊ D29×D13⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C13×C29C22×C3
LCSG ▷ C5×C13×C29
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1885

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22620, 54);