Finite Group Databasebeta

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C3×C5⋊(C17⋊(D13⋊C3)) #34091045

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

Aliases

direct productC3×C5⋊(C17⋊(D13⋊C3))
unambiguous semidirect productC5⋊(C3×C17⋊(D13⋊C3))
unambiguous semidirect productC17⋊(C3×C5⋊(D13⋊C3))
unambiguous semidirect product(C13⋊C3)⋊(C3×D85)
unambiguous semidirect productD1105⋊C32
unambiguous semidirect product(C3×D1105)⋊C3

Splittings

Fitting, socleC3×C5×C13×C17 ⋊ C2×C3
derived, HallC5×C13×C17 ⋊ C2×C32
HallC3×C5×C17×C13⋊C3 ⋊ C2
HallD1105 ⋊ C32
HallC3×C17×C13⋊C3 ⋊ D5
HallC3×C5×C13⋊C3 ⋊ D17
HallC13×C17 ⋊ C32×D5
HallC3×C13⋊C3 ⋊ D85
HallC5×C17 ⋊ C3×D13⋊C3
HallC5×C13 ⋊ C32×D17
SylowC17 ⋊ C3×C5⋊(D13⋊C3)
SylowC13 ⋊ C32×D85
SylowC5 ⋊ C3×C17⋊(D13⋊C3)

Subgroups

subgroupG/H
center, hypercenterC3C5⋊(C17⋊(D13⋊C3))
commutator, cosocle, hypocenterC5×C13×C17C2×C32
FrattiniC1G
Fitting, socleC3×C5×C13×C17C2×C3
LCSG ▷ C5×C13×C17
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3315

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 30);