Finite Group Databasebeta

← Prev (#46777915) Next (#46777917) →

D17×D495 #46777916

order33660
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD17×D495
unambiguous semidirect product(C5×D17)⋊D99
unambiguous semidirect product(C9×D17)⋊D55
unambiguous semidirect product(C11×D17)⋊D45

Splittings

Fitting, derived, HallC5×C9×C11×C17 ⋊ C22
HallC9×C11×C17 ⋊ C2×D5
HallC5×C11×C17 ⋊ C2×D9
HallC5×C9×C17 ⋊ C2×D11
HallC5×C9×C11 ⋊ C2×D17
HallC11×C17 ⋊ C2×D45
HallC9×C17 ⋊ C2×D55
HallC9×C11 ⋊ D5×D17
HallC5×C17 ⋊ C2×D99
HallC5×C11 ⋊ D9×D17
HallC5×C9 ⋊ D11×D17
SylowC17 ⋊ C2×D495
SylowC11 ⋊ D17×D45
SylowC9 ⋊ D17×D55
SylowC5 ⋊ D17×D99

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC5×C9×C11×C17C22
FrattiniC3D17×D165
socleC3×C5×C11×C17C2×D3
LCSG ▷ C5×C9×C11×C17
UCSC1

120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8415

Conjugacy classes & character table

2490 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 84);