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C17×D15×C13⋊C3 #34091054

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

Aliases

direct productC17×D15×C13⋊C3
unambiguous semidirect productC3⋊(D5×C17×C13⋊C3)
unambiguous semidirect productC5⋊(D3×C17×C13⋊C3)
unambiguous semidirect product(C13×D15)⋊(C3×C17)
unambiguous semidirect product(C13×C17×D15)⋊C3

Splittings

Fitting, socleC3×C5×C13×C17 ⋊ C2×C3
derivedC3×C5×C13 ⋊ C2×C3×C17
HallC3×C5×C17×C13⋊C3 ⋊ C2
HallC3×C17×C13⋊C3 ⋊ D5
HallC5×C13×C17 ⋊ C3×D3
HallC3×C5×C13⋊C3 ⋊ C2×C17
HallC13×C17 ⋊ C3×D15
HallC3×C13⋊C3 ⋊ D5×C17
HallC5×C17 ⋊ D3×C13⋊C3
HallC5×C13 ⋊ C3×D3×C17
SylowC13 ⋊ C3×C17×D15
SylowC5 ⋊ D3×C17×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC17D15×C13⋊C3
commutator, cosocle, hypocenterC3×C5×C13C2×C3×C17
FrattiniC1G
Fitting, socleC3×C5×C13×C17C2×C3
LCSG ▷ C3×C5×C13
UCSC1 ◁ C17

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3315

Conjugacy classes & character table

1071 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 39);