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C29×D15×C13⋊C3 #46800253

order33930
automorphism?
homologyAbelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×D15×C13⋊C3
unambiguous semidirect productC3⋊(D5×C29×C13⋊C3)
unambiguous semidirect productC5⋊(D3×C29×C13⋊C3)
unambiguous semidirect product(C13×D15)⋊(C3×C29)
unambiguous semidirect product(C13×C29×D15)⋊C3

Splittings

Fitting, socleC3×C5×C13×C29 ⋊ C2×C3
derivedC3×C5×C13 ⋊ C2×C3×C29
HallC3×C5×C29×C13⋊C3 ⋊ C2
HallC3×C29×C13⋊C3 ⋊ D5
HallC5×C13×C29 ⋊ C3×D3
HallC3×C5×C13⋊C3 ⋊ C2×C29
HallC13×C29 ⋊ C3×D15
HallC5×C29 ⋊ D3×C13⋊C3
HallC3×C13⋊C3 ⋊ D5×C29
HallC5×C13 ⋊ C3×D3×C29
SylowC13 ⋊ C3×C29×D15
SylowC5 ⋊ D3×C29×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC29D15×C13⋊C3
commutator, cosocle, hypocenterC3×C5×C13C2×C3×C29
FrattiniC1G
Fitting, socleC3×C5×C13×C29C2×C3
LCSG ▷ C3×C5×C13
UCSC1 ◁ C29

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5655

Conjugacy classes & character table

1827 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33930, 39);