Finite Group Databasebeta

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C9×D17×D55 #46777892

order33660
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC9×D17×D55
unambiguous semidirect product(C5×D17)⋊(C9×D11)
unambiguous semidirect product(C11×D17)⋊(C9×D5)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC9D17×D55
commutator, hypocenterC5×C11×C17C22×C9
FrattiniC3C3×D17×D55
FittingC5×C9×C11×C17C22
socle, cosocleC3×C5×C11×C17C22×C3
prime radicalC3×D17×D55C3
LCSG ▷ C5×C11×C17
UCSC1 ◁ C9

120 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 48 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

2610 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 60);