Finite Group Databasebeta

← Prev (#22578797) Next (#22578799) →

C5×C22⋊(C49⋊C9) #22578798

order8820
automorphism?
homologyAbelianization (H1) = C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC5×C22⋊(C49⋊C9)
unambiguous semidirect productC22⋊(C5×C49⋊C9)
unambiguous semidirect product(C22×C5)⋊(C49⋊C9)
unambiguous semidirect productC49⋊(C5×C22⋊C9)
unambiguous semidirect product(C5×C49)⋊(C22⋊C9)

Splittings

derived, HallC22×C49 ⋊ C5×C9
HallC22×C5×C49 ⋊ C9
HallC5×C49 ⋊ C22⋊C9
SylowC49 ⋊ C5×C22⋊C9
HallC22×C5 ⋊ C49⋊C9
SylowC22 ⋊ C5×C49⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C5C22⋊(C49⋊C3)
commutator, hypocenterC22×C49C5×C9
FrattiniC3×C7C5×C22⋊ΓL(1,𝔽8)
FittingC22×C3×C5×C49C3
socleC22×C3×C5×C7ΓL(1,𝔽8)
LCSG ▷ C22×C49
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1020 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8820, 33);