Finite Group Databasebeta

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C2×C11×AGL(1,𝔽31) #35205684

order20460
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×AGL(1,𝔽31)
unambiguous semidirect product(D31⋊C3)⋊(C2×C5×C11)
unambiguous semidirect product(D31⋊C5)⋊(C2×C3×C11)
unambiguous semidirect product(C2×D31⋊C3)⋊(C5×C11)
unambiguous semidirect product((C31⋊C3)⋊C5)⋊(C22×C11)
unambiguous semidirect product(C2×D31⋊C5)⋊(C3×C11)
unambiguous semidirect product(C2×(C31⋊C3)⋊C5)⋊(C2×C11)
unambiguous semidirect product(C2×C11×D31⋊C5)⋊C3

Splittings

Fitting, socleC2×C11×C31 ⋊ C2×C3×C5
derived, SylowC31 ⋊ C22×C3×C5×C11
HallC2×C11×D31⋊C5 ⋊ C3
HallC11×(C31⋊C3)⋊C5 ⋊ C22
HallC2×C11×D31⋊C3 ⋊ C5
HallC11×ΓL(1,𝔽32) ⋊ C22×C3
HallC2×C11×D31 ⋊ C3×C5
HallC11×C31⋊C3 ⋊ C22×C5
HallC2×D31⋊C5 ⋊ C3×C11
Hall(C31⋊C3)⋊C5 ⋊ C22×C11
HallC2×D31⋊C3 ⋊ C5×C11
HallC11×C31 ⋊ C22×C3×C5
HallΓL(1,𝔽32) ⋊ C22×C3×C11
HallC2×D31 ⋊ C3×C5×C11
HallC31⋊C3 ⋊ C22×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C11AGL(1,𝔽31)
commutator, cosocle, hypocenterC31C22×C3×C5×C11
FrattiniC1G
Fitting, socleC2×C11×C31C2×C3×C5
LCSG ▷ C31
UCSC1 ◁ C2×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 682

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20460, 104);