Finite Group Databasebeta

← Prev (#22548938) Next (#22548940) →

C11×C22⋊(C61⋊C3) #22548939

order8052
automorphism?
homologyAbelianization (H1) = C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×C22⋊(C61⋊C3)
unambiguous semidirect productC22⋊(C11×C61⋊C3)
unambiguous semidirect product(C22×C11)⋊(C61⋊C3)
unambiguous semidirect productC61⋊(C11×A4)
unambiguous semidirect product(C11×C61)⋊A4

Splittings

Fitting, socle, HallC22×C11×C61 ⋊ C3
derived, HallC22×C61 ⋊ C3×C11
HallC11×C61 ⋊ A4
SylowC61 ⋊ C11×A4
HallC22×C11 ⋊ C61⋊C3
SylowC22 ⋊ C11×C61⋊C3

Subgroups

subgroupG/H
center, hypercenterC11C22⋊(C61⋊C3)
commutator, hypocenterC22×C61C3×C11
FrattiniC1G
Fitting, socleC22×C11×C61C3
LCSG ▷ C22×C61
UCSC1 ◁ C11

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

924 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×A4×C61⋊C3, C3×C11×C22⋊(C61⋊C3)
maximal normal subgroup ofC11×A4×C61⋊C3, C3×C11×C22⋊(C61⋊C3)
maximal quotient ofC11×C22⋊(C61⋊C9), C3×C11×C22⋊(C61⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8052, 31);