Finite Group Databasebeta

← Prev (#46777852) Next (#46777854) →

C17×Dic9×C11⋊C5 #46777853

order33660
automorphism?
homologyAbelianization (H1) = C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×Dic9×C11⋊C5
unambiguous semidirect productC9⋊(C4×C17×C11⋊C5)
unambiguous semidirect product(C11×Dic9)⋊(C5×C17)
unambiguous semidirect product(C11×C17×Dic9)⋊C5

Splittings

derived, HallC9×C11 ⋊ C4×C5×C17
HallC9×C17×C11⋊C5 ⋊ C4
HallC11×C17×Dic9 ⋊ C5
HallC9×C11×C17 ⋊ C4×C5
HallC9×C11⋊C5 ⋊ C4×C17
HallC11×Dic9 ⋊ C5×C17
HallC11×C17 ⋊ C5×Dic9
HallC9×C17 ⋊ C4×C11⋊C5
SylowC11 ⋊ C5×C17×Dic9
SylowC9 ⋊ C4×C17×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C17D9×C11⋊C5
commutator, hypocenterC9×C11C4×C5×C17
FrattiniC2×C3D3×C17×C11⋊C5
FittingC2×C9×C11×C17C2×C5
socleC2×C3×C11×C17C5×D3
prime radicalC2×C3×C17×C11⋊C5D3
cosocleC2×C9×C11C2×C5×C17
LCSG ▷ C9×C11
UCSC1 ◁ C2×C17

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6732

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(33660, 21);