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D11×AGL(1,𝔽31) #35205683

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

Aliases

direct productD11×AGL(1,𝔽31)
unambiguous semidirect product(D31⋊C3)⋊(C5×D11)
unambiguous semidirect product(D31⋊C5)⋊(C3×D11)
unambiguous semidirect product(D11×D31⋊C5)⋊C3
unambiguous semidirect product(C11×AGL(1,𝔽31))⋊C2
unambiguous semidirect product(D11×(C31⋊C3)⋊C5)⋊C2
unambiguous semidirect product(((C31⋊C3)⋊C5)⋊D11)⋊C2

Splittings

Fitting, socle, derived, HallC11×C31 ⋊ C22×C3×C5
HallD11×D31⋊C5 ⋊ C3
HallC11×(C31⋊C3)⋊C5 ⋊ C22
HallD11×D31⋊C3 ⋊ C5
HallC11×ΓL(1,𝔽32) ⋊ C22×C3
HallD11×D31 ⋊ C3×C5
HallC11×C31⋊C3 ⋊ C22×C5
Hall(C31⋊C3)⋊C5 ⋊ C2×D11
HallΓL(1,𝔽32) ⋊ C2×C3×D11
HallC31⋊C3 ⋊ C2×C5×D11
SylowC31 ⋊ C2×C3×C5×D11
SylowC11 ⋊ C2×AGL(1,𝔽31)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C31C22×C3×C5
LCSG ▷ C11×C31
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 341

Conjugacy classes & character table

217 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20460, 103);