Finite Group Databasebeta

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C2×C11×D711 #44530865

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

Aliases

direct productC2×C11×D711
unambiguous semidirect product(C2×C9)⋊(C11×D79)
unambiguous semidirect product(C2×C79)⋊(C11×D9)

Splittings

FittingC2×C9×C11×C79 ⋊ C2
derived, HallC9×C79 ⋊ C22×C11
HallC9×C11×C79 ⋊ C22
HallC11×C79 ⋊ C2×D9
HallC9×C11 ⋊ C2×D79
SylowC79 ⋊ C2×C11×D9
SylowC9 ⋊ C2×C11×D79

Subgroups

subgroupG/H
center, hypercenterC2×C11D711
commutator, cosocle, hypocenterC9×C79C22×C11
FrattiniC3C2×C11×D237
FittingC2×C9×C11×C79C2
socleC2×C3×C11×C79D3
LCSG ▷ C9×C79
UCSC1 ◁ C2×C11

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15642

Conjugacy classes & character table

7854 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31284, 30);