Finite Group Databasebeta

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C5×C11×C17×C22⋊C9 #46777937

order33660
automorphism?
homologyAbelianization (H1) = C5×C9×C11×C17 · Schur multiplier (H2) = C2

Aliases

direct productC5×C11×C17×C22⋊C9
unambiguous semidirect productC22⋊(C5×C9×C11×C17)
unambiguous semidirect product(C22×C5)⋊(C9×C11×C17)
unambiguous semidirect product(C22×C17)⋊(C5×C9×C11)
unambiguous semidirect product(C22×C5×C11)⋊(C9×C17)
unambiguous semidirect product(C22×C5×C17)⋊(C9×C11)
unambiguous semidirect product(C22×C5×C11×C17)⋊C9

Splittings

derived, SylowC22 ⋊ C5×C9×C11×C17
HallC22×C5×C11×C17 ⋊ C9
HallC22×C11×C17 ⋊ C5×C9
HallC22×C5×C17 ⋊ C9×C11
HallC22×C5×C11 ⋊ C9×C17
HallC22×C17 ⋊ C5×C9×C11
HallC22×C11 ⋊ C5×C9×C17
HallC22×C5 ⋊ C9×C11×C17

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11×C17A4
commutator, hypocenterC22C5×C9×C11×C17
FrattiniC3C5×C11×A4×C17
Fitting, socle, prime radicalC22×C3×C5×C11×C17C3
cosocleC22×C3C3×C5×C11×C17
LCSG ▷ C22
UCSC1 ◁ C3×C5×C11×C17

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16830

Conjugacy classes & character table

11220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 105);