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C2×C31⋊C3×AGL(1,𝔽11) #35205694

order20460
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C31⋊C3×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C2×C5×C31⋊C3)
unambiguous semidirect product(C2×D11)⋊(C5×C31⋊C3)
unambiguous semidirect product(C11⋊C5)⋊(C22×C31⋊C3)
unambiguous semidirect product(C2×C11⋊C5)⋊(C2×C31⋊C3)
unambiguous semidirect product(C2×C31×AGL(1,𝔽11))⋊C3

Splittings

Fitting, socleC2×C11×C31 ⋊ C2×C3×C5
derived, HallC11×C31 ⋊ C22×C3×C5
HallC2×C31×AGL(1,𝔽11) ⋊ C3
HallC11⋊C5×C31⋊C3 ⋊ C22
HallC2×D11×C31⋊C3 ⋊ C5
HallC31×C11⋊C5 ⋊ C22×C3
HallC2×D11×C31 ⋊ C3×C5
HallC11×C31⋊C3 ⋊ C22×C5
HallC11⋊C5 ⋊ C22×C31⋊C3
HallC2×D11 ⋊ C5×C31⋊C3
SylowC31 ⋊ C2×C3×AGL(1,𝔽11)
SylowC11 ⋊ C22×C5×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C31⋊C3×AGL(1,𝔽11)
commutator, cosocle, hypocenterC11×C31C22×C3×C5
FrattiniC1G
Fitting, socleC2×C11×C31C2×C3×C5
LCSG ▷ C11×C31
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 682

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20460, 114);