Finite Group Databasebeta

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C3×C5×C17×D13⋊C3 #34091041

order19890
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C17 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C17×D13⋊C3
unambiguous semidirect productD13⋊(C32×C5×C17)
unambiguous semidirect product(C13⋊C3)⋊(C2×C3×C5×C17)
unambiguous semidirect product(C3×D13)⋊(C3×C5×C17)
unambiguous semidirect product(C5×D13)⋊(C32×C17)
unambiguous semidirect product(C3×C5×D13)⋊(C3×C17)
unambiguous semidirect product(C17×D13)⋊(C32×C5)
unambiguous semidirect product(C3×C17×D13)⋊(C3×C5)
unambiguous semidirect product(C5×C17×D13)⋊C32
unambiguous semidirect product(C3×C5×C17×D13)⋊C3

Splittings

Fitting, socleC3×C5×C13×C17 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C32×C5×C17
HallC3×C5×C17×C13⋊C3 ⋊ C2
HallC5×C17×D13 ⋊ C32
HallC3×C17×C13⋊C3 ⋊ C2×C5
HallC5×C13×C17 ⋊ C2×C32
HallC3×C5×C13⋊C3 ⋊ C2×C17
HallC17×D13 ⋊ C32×C5
HallC13×C17 ⋊ C2×C32×C5
HallC5×D13 ⋊ C32×C17
HallC3×C13⋊C3 ⋊ C2×C5×C17
HallC5×C13 ⋊ C2×C32×C17
HallD13 ⋊ C32×C5×C17

Subgroups

subgroupG/H
center, hypercenterC3×C5×C17D13⋊C3
commutator, cosocle, hypocenterC13C2×C32×C5×C17
FrattiniC1G
Fitting, socleC3×C5×C13×C17C2×C3
LCSG ▷ C13
UCSC1 ◁ C3×C5×C17

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3315

Conjugacy classes & character table

2040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 26);