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C5×C13⋊C3×D51 #34091051

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

Aliases

direct productC5×C13⋊C3×D51
unambiguous semidirect productC3⋊(C5×D17×C13⋊C3)
unambiguous semidirect productC17⋊(C5×D3×C13⋊C3)
unambiguous semidirect product(C13×D51)⋊(C3×C5)
unambiguous semidirect product(C5×C13×D51)⋊C3

Splittings

Fitting, socleC3×C5×C13×C17 ⋊ C2×C3
derivedC3×C13×C17 ⋊ C2×C3×C5
HallC3×C5×C17×C13⋊C3 ⋊ C2
HallC3×C17×C13⋊C3 ⋊ C2×C5
HallC5×C13×C17 ⋊ C3×D3
HallC3×C5×C13⋊C3 ⋊ D17
HallC13×C17 ⋊ C3×C5×D3
HallC3×C13⋊C3 ⋊ C5×D17
HallC5×C17 ⋊ D3×C13⋊C3
HallC5×C13 ⋊ C3×D51
SylowC17 ⋊ C5×D3×C13⋊C3
SylowC13 ⋊ C3×C5×D51

Subgroups

subgroupG/H
center, hypercenterC5C13⋊C3×D51
commutator, cosocle, hypocenterC3×C13×C17C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C13×C17C2×C3
LCSG ▷ C3×C13×C17
UCSC1 ◁ C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3315

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 36);