Finite Group Databasebeta

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C11×A4×C79⋊C3 #44530898

order31284
automorphism?
homologyAbelianization (H1) = C32×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC11×A4×C79⋊C3
unambiguous semidirect product(C22×C79⋊C3)⋊(C3×C11)
unambiguous semidirect product(A4×C79)⋊(C3×C11)
unambiguous semidirect product(C22⋊(C79⋊C3))⋊(C3×C11)
unambiguous semidirect product(C11×C22⋊(C79⋊C3))⋊C3
unambiguous semidirect product(C11×A4×C79)⋊C3
unambiguous semidirect product(C22×C11×C79⋊C3)⋊C3

Splittings

Fitting, socle, HallC22×C11×C79 ⋊ C32
derived, HallC22×C79 ⋊ C32×C11
HallC11×C79 ⋊ C3×A4
SylowC79 ⋊ C3×C11×A4
HallC22×C11 ⋊ C3×C79⋊C3
SylowC22 ⋊ C3×C11×C79⋊C3

Subgroups

subgroupG/H
center, hypercenterC11A4×C79⋊C3
commutator, cosocle, hypocenterC22×C79C32×C11
FrattiniC1G
Fitting, socleC22×C11×C79C32
LCSG ▷ C22×C79
UCSC1 ◁ C11

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3476

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31284, 63);