Finite Group Databasebeta

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C11⋊C5×C9⋊#595 #46777867

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

Aliases

direct productC11⋊C5×C9⋊#595
unambiguous semidirect productC9⋊(C11⋊C5×#595)
unambiguous semidirect product(C11×C9⋊#595)⋊C5

Splittings

Fitting, derived, HallC9×C11×C17 ⋊ C4×C5
HallC9×C17×C11⋊C5 ⋊ C4
HallC11×C9⋊#595 ⋊ C5
HallC17×C11⋊C5 ⋊ Dic9
HallC9×C11⋊C5 ⋊ #595
HallC11×C17 ⋊ C5×Dic9
HallC9×C17 ⋊ C4×C11⋊C5
HallC9×C11 ⋊ C5×#595
SylowC17 ⋊ Dic9×C11⋊C5
SylowC11 ⋊ C5×C9⋊#595
SylowC9 ⋊ C11⋊C5×#595

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, hypocenterC9×C11×C17C4×C5
FrattiniC3C11⋊C5×C3⋊#595
socleC3×C11×C17C5×Dic3
prime radicalC3×D17×C11⋊C5D3
cosocleC9×C11×D17C2×C5
LCSG ▷ C9×C11×C17
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1683

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 35);