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C13⋊C3×D435 #46800254

order33930
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC13⋊C3×D435
unambiguous semidirect productC3⋊(C13⋊C3×D145)
unambiguous semidirect productC5⋊(C13⋊C3×D87)
unambiguous semidirect productC29⋊(D15×C13⋊C3)
unambiguous semidirect product(C13×D435)⋊C3

Splittings

Fitting, socle, derivedC3×C5×C13×C29 ⋊ C2×C3
HallC3×C5×C29×C13⋊C3 ⋊ C2
HallC3×C29×C13⋊C3 ⋊ D5
HallC5×C13×C29 ⋊ C3×D3
HallC3×C5×C13⋊C3 ⋊ D29
HallC13×C29 ⋊ C3×D15
HallC5×C29 ⋊ D3×C13⋊C3
HallC3×C13⋊C3 ⋊ D145
HallC5×C13 ⋊ C3×D87
SylowC29 ⋊ D15×C13⋊C3
SylowC13 ⋊ C3×D435
SylowC5 ⋊ C13⋊C3×D87

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C13×C29C2×C3
LCSG ▷ C3×C5×C13×C29
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5655

Conjugacy classes & character table

1533 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33930, 40);