Finite Group Databasebeta

← Prev (#34091035) Next (#34091037) →

D5×C17×C13⋊C9 #34091036

order19890
automorphism?
homologyAbelianization (H1) = C2×C9×C17 · Schur multiplier (H2) = C1

Aliases

direct productD5×C17×C13⋊C9
unambiguous semidirect productC5⋊(C2×C17×C13⋊C9)
unambiguous semidirect product(D5×C13)⋊(C9×C17)
unambiguous semidirect product(D5×C13×C17)⋊C9

Splittings

derived, HallC5×C13 ⋊ C2×C9×C17
HallC5×C17×C13⋊C9 ⋊ C2
HallD5×C13×C17 ⋊ C9
HallC5×C13×C17 ⋊ C2×C9
HallC5×C13⋊C9 ⋊ C2×C17
HallC13×C17 ⋊ C9×D5
HallD5×C13 ⋊ C9×C17
HallC5×C17 ⋊ C2×C13⋊C9
SylowC13 ⋊ C9×D5×C17
SylowC5 ⋊ C2×C17×C13⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C17D5×C13⋊C3
commutator, hypocenterC5×C13C2×C9×C17
FrattiniC3D5×C17×C13⋊C3
Fitting, socleC3×C5×C13×C17C2×C3
prime radicalC3×D5×C13×C17C3
cosocleC3×C5×C13C2×C3×C17
LCSG ▷ C5×C13
UCSC1 ◁ C3×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9945

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, 21);