Finite Group Databasebeta

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C11×A4×C31⋊C3 #27134018

order12276
automorphism?
homologyAbelianization (H1) = C32×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC11×A4×C31⋊C3
unambiguous semidirect product(C22×C31⋊C3)⋊(C3×C11)
unambiguous semidirect product(A4×C31)⋊(C3×C11)
unambiguous semidirect product(C22⋊(C31⋊C3))⋊(C3×C11)
unambiguous semidirect product(C22×C11×C31⋊C3)⋊C3
unambiguous semidirect product(C11×A4×C31)⋊C3
unambiguous semidirect product(C11×C22⋊(C31⋊C3))⋊C3

Splittings

Fitting, socle, HallC22×C11×C31 ⋊ C32
derived, HallC22×C31 ⋊ C32×C11
HallC11×C31 ⋊ C3×A4
HallC22×C11 ⋊ C3×C31⋊C3
SylowC31 ⋊ C3×C11×A4
SylowC22 ⋊ C3×C11×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC11A4×C31⋊C3
commutator, cosocle, hypocenterC22×C31C32×C11
FrattiniC1G
Fitting, socleC22×C11×C31C32
LCSG ▷ C22×C31
UCSC1 ◁ C11

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12276, 63);