Finite Group Databasebeta

← Prev (#44568420) Next (#44568422) →

C5×C11×C22⋊(C49⋊C3) #44568421

order32340
automorphism?
homologyAbelianization (H1) = C3×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC5×C11×C22⋊(C49⋊C3)
unambiguous semidirect productC22⋊(C5×C11×C49⋊C3)
unambiguous semidirect product(C22×C5)⋊(C11×C49⋊C3)
unambiguous semidirect productC49⋊(C5×C11×A4)
unambiguous semidirect product(C22×C5×C11)⋊(C49⋊C3)
unambiguous semidirect product(C5×C49)⋊(C11×A4)
unambiguous semidirect product(C5×C11×C49)⋊A4

Splittings

Fitting, HallC22×C5×C11×C49 ⋊ C3
derived, HallC22×C49 ⋊ C3×C5×C11
HallC5×C11×C49 ⋊ A4
HallC22×C11×C49 ⋊ C3×C5
HallC22×C5×C49 ⋊ C3×C11
HallC11×C49 ⋊ C5×A4
HallC5×C49 ⋊ C11×A4
HallC22×C5×C11 ⋊ C49⋊C3
SylowC49 ⋊ C5×C11×A4
HallC22×C11 ⋊ C5×C49⋊C3
HallC22×C5 ⋊ C11×C49⋊C3
SylowC22 ⋊ C5×C11×C49⋊C3

Subgroups

subgroupG/H
center, hypercenterC5×C11C22⋊(C49⋊C3)
commutator, cosocle, hypocenterC22×C49C3×C5×C11
FrattiniC7C5×C11×C22⋊ΓL(1,𝔽8)
FittingC22×C5×C11×C49C3
socleC22×C5×C7×C11ΓL(1,𝔽8)
LCSG ▷ C22×C49
UCSC1 ◁ C5×C11

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10780

Conjugacy classes & character table

3740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 123);