Finite Group Databasebeta

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C3×D5×C17×C13⋊C3 #34091046

order19890
automorphism?
homologyAbelianization (H1) = C2×C32×C17 · Schur multiplier (H2) = C3

Aliases

direct productC3×D5×C17×C13⋊C3
unambiguous semidirect productC5⋊(C2×C3×C17×C13⋊C3)
unambiguous semidirect product(D5×C13)⋊(C32×C17)
unambiguous semidirect product(C3×D5×C13)⋊(C3×C17)
unambiguous semidirect product(D5×C13×C17)⋊C32
unambiguous semidirect product(C3×D5×C13×C17)⋊C3

Splittings

Fitting, socleC3×C5×C13×C17 ⋊ C2×C3
derived, HallC5×C13 ⋊ C2×C32×C17
HallC3×C5×C17×C13⋊C3 ⋊ C2
HallD5×C13×C17 ⋊ C32
HallC5×C13×C17 ⋊ C2×C32
HallC3×C5×C13⋊C3 ⋊ C2×C17
HallC13×C17 ⋊ C32×D5
HallD5×C13 ⋊ C32×C17
HallC5×C17 ⋊ C2×C3×C13⋊C3
SylowC13 ⋊ C32×D5×C17
SylowC5 ⋊ C2×C3×C17×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C17D5×C13⋊C3
commutator, cosocle, hypocenterC5×C13C2×C32×C17
FrattiniC1G
Fitting, socleC3×C5×C13×C17C2×C3
LCSG ▷ C5×C13
UCSC1 ◁ C3×C17

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3315

Conjugacy classes & character table

1428 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 31);