Finite Group Databasebeta

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C5×D3×C17×C13⋊C3 #34091050

order19890
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×D3×C17×C13⋊C3
unambiguous semidirect productC3⋊(C2×C5×C17×C13⋊C3)
unambiguous semidirect product(D3×C13)⋊(C3×C5×C17)
unambiguous semidirect product(C5×D3×C13)⋊(C3×C17)
unambiguous semidirect product(D3×C13×C17)⋊(C3×C5)
unambiguous semidirect product(C5×D3×C13×C17)⋊C3

Splittings

Fitting, socleC3×C5×C13×C17 ⋊ C2×C3
derivedC3×C13 ⋊ C2×C3×C5×C17
HallC3×C5×C17×C13⋊C3 ⋊ C2
HallC3×C17×C13⋊C3 ⋊ C2×C5
HallC5×C13×C17 ⋊ C3×D3
HallC3×C5×C13⋊C3 ⋊ C2×C17
HallC13×C17 ⋊ C3×C5×D3
HallC3×C13⋊C3 ⋊ C2×C5×C17
HallC5×C13 ⋊ C3×D3×C17
SylowC13 ⋊ C3×C5×D3×C17

Subgroups

subgroupG/H
center, hypercenterC5×C17D3×C13⋊C3
commutator, cosocle, hypocenterC3×C13C2×C3×C5×C17
FrattiniC1G
Fitting, socleC3×C5×C13×C17C2×C3
LCSG ▷ C3×C13
UCSC1 ◁ C5×C17

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3315

Conjugacy classes & character table

1785 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 35);