Finite Group Databasebeta

← Prev (#22554321) Next (#22554323) →

C9×C17×C11⋊C5 #22554322

order8415
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C5×C9×C17 · Schur multiplier (H2) = C1

Aliases

direct productC9×C17×C11⋊C5
unambiguous semidirect productC11⋊(C5×C9×C17)
unambiguous semidirect product(C9×C11)⋊(C5×C17)
unambiguous semidirect product(C11×C17)⋊(C5×C9)
unambiguous semidirect product(C9×C11×C17)⋊C5

Splittings

Fitting, HallC9×C11×C17 ⋊ C5
derived, SylowC11 ⋊ C5×C9×C17
HallC11×C17 ⋊ C5×C9
HallC9×C11 ⋊ C5×C17

Subgroups

subgroupG/H
center, hypercenterC9×C17C11⋊C5
commutator, hypocenterC11C5×C9×C17
FrattiniC3C3×C17×C11⋊C5
FittingC9×C11×C17C5
socleC3×C11×C17C3×C5
LCSG ▷ C11
UCSC1 ◁ C9×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1071 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C9×C17×C11⋊C5, C9×D17×C11⋊C5, C9×C17×AGL(1,𝔽11), …
maximal normal subgroup ofC2×C9×C17×C11⋊C5, C9×D17×C11⋊C5, C9×C17×AGL(1,𝔽11), …
maximal quotient ofC2×C9×C17×C11⋊C5, C17×C22⋊C9×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8415, 2);