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C2×C3×C47×AGL(1,𝔽11) #44526631

order31020
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C47 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C47×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C2×C3×C5×C47)
unambiguous semidirect product(C2×D11)⋊(C3×C5×C47)
unambiguous semidirect product(C11⋊C5)⋊(C22×C3×C47)
unambiguous semidirect product(C2×C11⋊C5)⋊(C2×C3×C47)
unambiguous semidirect product(C2×C3×D11)⋊(C5×C47)
unambiguous semidirect product(C2×D11×C47)⋊(C3×C5)
unambiguous semidirect product(C2×C3×D11×C47)⋊C5

Splittings

Fitting, socleC2×C3×C11×C47 ⋊ C2×C5
derived, SylowC11 ⋊ C22×C3×C5×C47
HallC3×C47×C11⋊C5 ⋊ C22
HallC2×C3×D11×C47 ⋊ C5
HallC47×C11⋊C5 ⋊ C22×C3
HallC2×D11×C47 ⋊ C3×C5
HallC3×C11×C47 ⋊ C22×C5
HallC11×C47 ⋊ C22×C3×C5
HallC3×C11⋊C5 ⋊ C22×C47
HallC2×C3×D11 ⋊ C5×C47
HallC11⋊C5 ⋊ C22×C3×C47
HallC2×D11 ⋊ C3×C5×C47
HallC3×C11 ⋊ C22×C5×C47

Subgroups

subgroupG/H
center, hypercenterC2×C3×C47AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C22×C3×C5×C47
FrattiniC1G
Fitting, socleC2×C3×C11×C47C2×C5
LCSG ▷ C11
UCSC1 ◁ C2×C3×C47

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3102

Conjugacy classes & character table

3102 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 34);