Finite Group Databasebeta

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A4×C17×C11⋊C5 #26014361

order11220
automorphism?
homologyAbelianization (H1) = C3×C5×C17 · Schur multiplier (H2) = C2

Aliases

direct productA4×C17×C11⋊C5
unambiguous semidirect productC22⋊(C3×C17×C11⋊C5)
unambiguous semidirect productC11⋊(C5×A4×C17)
unambiguous semidirect product(C22×C17)⋊(C3×C11⋊C5)
unambiguous semidirect product(C11×A4)⋊(C5×C17)
unambiguous semidirect product(C11×C17)⋊(C5×A4)
unambiguous semidirect product(C22×C11⋊C5)⋊(C3×C17)
unambiguous semidirect product(C11×A4×C17)⋊C5
unambiguous semidirect product(C22×C17×C11⋊C5)⋊C3

Splittings

Fitting, socle, HallC22×C11×C17 ⋊ C3×C5
derived, HallC22×C11 ⋊ C3×C5×C17
HallC22×C17×C11⋊C5 ⋊ C3
HallC11×A4×C17 ⋊ C5
HallC22×C11⋊C5 ⋊ C3×C17
HallC11×C17 ⋊ C5×A4
HallC11×A4 ⋊ C5×C17
HallC22×C17 ⋊ C3×C11⋊C5
SylowC11 ⋊ C5×A4×C17
SylowC22 ⋊ C3×C17×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC17A4×C11⋊C5
commutator, cosocle, hypocenterC22×C11C3×C5×C17
FrattiniC1G
Fitting, socleC22×C11×C17C3×C5
LCSG ▷ C22×C11
UCSC1 ◁ C17

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

476 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×A4×C17×C11⋊C5
maximal normal subgroup ofC3×A4×C17×C11⋊C5
maximal quotient ofC17×C22⋊C9×C11⋊C5, C3×A4×C17×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 37);