Finite Group Databasebeta

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C3×C5×C17⋊(D13⋊C3) #34091042

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

Aliases

direct productC3×C5×C17⋊(D13⋊C3)
unambiguous semidirect productC17⋊(C3×C5×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(C3×C5×D17)
unambiguous semidirect productD221⋊(C32×C5)
unambiguous semidirect product(C3×D221)⋊(C3×C5)
unambiguous semidirect product(C5×D221)⋊C32
unambiguous semidirect product(C3×C5×D221)⋊C3

Splittings

Fitting, socleC3×C5×C13×C17 ⋊ C2×C3
derived, HallC13×C17 ⋊ C2×C32×C5
HallC3×C5×C17×C13⋊C3 ⋊ C2
HallC5×D221 ⋊ C32
HallC3×C17×C13⋊C3 ⋊ C2×C5
HallC5×C13×C17 ⋊ C2×C32
HallC3×C5×C13⋊C3 ⋊ D17
HallD221 ⋊ C32×C5
HallC3×C13⋊C3 ⋊ C5×D17
HallC5×C17 ⋊ C3×D13⋊C3
HallC5×C13 ⋊ C32×D17
SylowC17 ⋊ C3×C5×D13⋊C3
SylowC13 ⋊ C32×C5×D17

Subgroups

subgroupG/H
center, hypercenterC3×C5C17⋊(D13⋊C3)
commutator, cosocle, hypocenterC13×C17C2×C32×C5
FrattiniC1G
Fitting, socleC3×C5×C13×C17C2×C3
LCSG ▷ C13×C17
UCSC1 ◁ C3×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3315

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 27);