Finite Group Databasebeta

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C2×C3×C11×D79⋊C3 #44530899

order31284
automorphism?
homologyAbelianization (H1) = C22×C32×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C11×D79⋊C3
unambiguous semidirect productD79⋊(C2×C32×C11)
unambiguous semidirect product(C79⋊C3)⋊(C22×C3×C11)
unambiguous semidirect product(C2×D79)⋊(C32×C11)
unambiguous semidirect product(C2×C79⋊C3)⋊(C2×C3×C11)
unambiguous semidirect product(C2×C3×D79)⋊(C3×C11)
unambiguous semidirect product(C2×C11×D79)⋊C32
unambiguous semidirect product(C2×C3×C11×D79)⋊C3

Splittings

Fitting, socleC2×C3×C11×C79 ⋊ C2×C3
derived, SylowC79 ⋊ C22×C32×C11
HallC3×C11×C79⋊C3 ⋊ C22
HallC2×C11×D79 ⋊ C32
HallC11×C79 ⋊ C22×C32
HallC3×C79⋊C3 ⋊ C22×C11
HallC2×D79 ⋊ C32×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11D79⋊C3
commutator, cosocle, hypocenterC79C22×C32×C11
FrattiniC1G
Fitting, socleC2×C3×C11×C79C2×C3
LCSG ▷ C79
UCSC1 ◁ C2×C3×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5214

Conjugacy classes & character table

1254 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31284, 64);