Finite Group Databasebeta

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C2×C32×C17×AGL(1,𝔽11) #46778026

order33660
automorphism?
homologyAbelianization (H1) = C22×C32×C5×C17 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×C17×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C2×C32×C5×C17)
unambiguous semidirect product(C2×D11)⋊(C32×C5×C17)
unambiguous semidirect product(C11⋊C5)⋊(C22×C32×C17)
unambiguous semidirect product(C2×C11⋊C5)⋊(C2×C32×C17)
unambiguous semidirect product(C2×C3×D11)⋊(C3×C5×C17)
unambiguous semidirect product(C2×C32×D11)⋊(C5×C17)
unambiguous semidirect product(C2×C17×D11)⋊(C32×C5)
unambiguous semidirect product(C2×C3×C17×D11)⋊(C3×C5)
unambiguous semidirect product(C2×C32×C17×D11)⋊C5

Splittings

Fitting, socleC2×C32×C11×C17 ⋊ C2×C5
derived, SylowC11 ⋊ C22×C32×C5×C17
HallC32×C17×C11⋊C5 ⋊ C22
HallC2×C32×C17×D11 ⋊ C5
HallC32×C11×C17 ⋊ C22×C5
HallC17×C11⋊C5 ⋊ C22×C32
HallC2×C17×D11 ⋊ C32×C5
HallC32×C11⋊C5 ⋊ C22×C17
HallC2×C32×D11 ⋊ C5×C17
HallC11×C17 ⋊ C22×C32×C5
HallC32×C11 ⋊ C22×C5×C17
HallC11⋊C5 ⋊ C22×C32×C17
HallC2×D11 ⋊ C32×C5×C17

Subgroups

subgroupG/H
center, hypercenterC2×C32×C17AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C22×C32×C5×C17
FrattiniC1G
Fitting, socleC2×C32×C11×C17C2×C5
LCSG ▷ C11
UCSC1 ◁ C2×C32×C17

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3366

Conjugacy classes & character table

3366 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 194);