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C11×C22⋊(C43⋊C3) #19150930

order5676
automorphism?
homologyAbelianization (H1) = C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×C22⋊(C43⋊C3)
unambiguous semidirect productC22⋊(C11×C43⋊C3)
unambiguous semidirect productC43⋊(C11×A4)
unambiguous semidirect product(C22×C11)⋊(C43⋊C3)
unambiguous semidirect product(C11×C43)⋊A4

Splittings

Fitting, socle, HallC22×C11×C43 ⋊ C3
derived, HallC22×C43 ⋊ C3×C11
HallC11×C43 ⋊ A4
HallC22×C11 ⋊ C43⋊C3
SylowC43 ⋊ C11×A4
SylowC22 ⋊ C11×C43⋊C3

Subgroups

subgroupG/H
center, hypercenterC11C22⋊(C43⋊C3)
commutator, hypocenterC22×C43C3×C11
FrattiniC1G
Fitting, socleC22×C11×C43C3
LCSG ▷ C22×C43
UCSC1 ◁ C11

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

660 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×A4×C43⋊C3, C3×C11×C22⋊(C43⋊C3), C11⋊C5×C22⋊(C43⋊C3), …
maximal normal subgroup ofC11×A4×C43⋊C3, C3×C11×C22⋊(C43⋊C3), C11⋊C5×C22⋊(C43⋊C3), …
maximal quotient ofC11×C22⋊(C43⋊C9), C3×C11×C22⋊(C43⋊C3), C5×C11×C22⋊(C43⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5676, 27);