Finite Group Databasebeta

← Prev (#46777921) Next (#46777923) →

D5×C11×D153 #46777922

order33660
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productD5×C11×D153
unambiguous semidirect product(C9×D5)⋊(C11×D17)
unambiguous semidirect product(D5×C17)⋊(C11×D9)

Splittings

Fitting, HallC5×C9×C11×C17 ⋊ C22
derived, HallC5×C9×C17 ⋊ C22×C11
HallC9×C11×C17 ⋊ C2×D5
HallC5×C11×C17 ⋊ C2×D9
HallC5×C9×C11 ⋊ C2×D17
HallC11×C17 ⋊ D5×D9
HallC9×C17 ⋊ C2×D5×C11
HallC9×C11 ⋊ D5×D17
HallC5×C17 ⋊ C2×C11×D9
HallC5×C11 ⋊ C2×D153
HallC5×C9 ⋊ C2×C11×D17
SylowC17 ⋊ D5×C11×D9
SylowC9 ⋊ D5×C11×D17
SylowC5 ⋊ C2×C11×D153

Subgroups

subgroupG/H
center, hypercenterC11D5×D153
commutator, cosocle, hypocenterC5×C9×C17C22×C11
FrattiniC3D5×C11×D51
FittingC5×C9×C11×C17C22
socleC3×C5×C11×C17C2×D3
LCSG ▷ C5×C9×C17
UCSC1 ◁ C11

120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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

3432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 90);