Finite Group Databasebeta

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C3×C17×C5⋊(D13⋊C3) #34091044

order19890
automorphism?
homologyAbelianization (H1) = C2×C32×C17 · Schur multiplier (H2) = C3

Aliases

direct productC3×C17×C5⋊(D13⋊C3)
unambiguous semidirect productC5⋊(C3×C17×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(C3×D5×C17)
unambiguous semidirect productD65⋊(C32×C17)
unambiguous semidirect product(C3×D65)⋊(C3×C17)
unambiguous semidirect product(C17×D65)⋊C32
unambiguous semidirect product(C3×C17×D65)⋊C3

Splittings

Fitting, socleC3×C5×C13×C17 ⋊ C2×C3
derived, HallC5×C13 ⋊ C2×C32×C17
HallC3×C5×C17×C13⋊C3 ⋊ C2
HallC17×D65 ⋊ C32
HallC3×C17×C13⋊C3 ⋊ D5
HallC5×C13×C17 ⋊ C2×C32
HallC3×C5×C13⋊C3 ⋊ C2×C17
HallC13×C17 ⋊ C32×D5
HallD65 ⋊ C32×C17
HallC3×C13⋊C3 ⋊ D5×C17
HallC5×C17 ⋊ C3×D13⋊C3
SylowC13 ⋊ C32×D5×C17
SylowC5 ⋊ C3×C17×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C17C5⋊(D13⋊C3)
commutator, cosocle, hypocenterC5×C13C2×C32×C17
FrattiniC1G
Fitting, socleC3×C5×C13×C17C2×C3
LCSG ▷ C5×C13
UCSC1 ◁ C3×C17

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3315

Conjugacy classes & character table

1122 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 29);