Finite Group Databasebeta

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C2×C17×C3⋊(C3⋊AGL(1,𝔽11)) #46778033

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

Aliases

direct productC2×C17×C3⋊(C3⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C3)⋊(C17×C3⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊(C17×C3⋊D3)
unambiguous semidirect product(C2×C3⋊D33)⋊(C5×C17)
unambiguous semidirect product(C2×C17×C3⋊D33)⋊C5

Splittings

Fitting, socleC2×C32×C11×C17 ⋊ C2×C5
derived, HallC32×C11 ⋊ C22×C5×C17
HallC32×C17×C11⋊C5 ⋊ C22
HallC2×C17×C3⋊D33 ⋊ C5
HallC32×C11×C17 ⋊ C22×C5
HallC17×C11⋊C5 ⋊ C2×C3⋊D3
HallC32×C11⋊C5 ⋊ C22×C17
HallC2×C3⋊D33 ⋊ C5×C17
HallC11×C17 ⋊ C2×C5×C3⋊D3
HallC32×C17 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×C17×C3⋊D3
SylowC11 ⋊ C2×C5×C17×C3⋊D3
SylowC32 ⋊ C2×C17×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC2×C17C3⋊(C3⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC32×C11C22×C5×C17
FrattiniC1G
Fitting, socleC2×C32×C11×C17C2×C5
LCSG ▷ C32×C11
UCSC1 ◁ C2×C17

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3366

Conjugacy classes & character table

1326 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 201);