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C2×C3×C17×AGL(1,𝔽11) #26014362

order11220
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C17 · Schur multiplier (H2) = C2

Aliases

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

Splittings

Fitting, socleC2×C3×C11×C17 ⋊ C2×C5
derived, SylowC11 ⋊ C22×C3×C5×C17
HallC3×C17×C11⋊C5 ⋊ C22
HallC2×C3×C17×D11 ⋊ C5
HallC17×C11⋊C5 ⋊ C22×C3
HallC2×C17×D11 ⋊ C3×C5
HallC3×C11×C17 ⋊ C22×C5
HallC11×C17 ⋊ C22×C3×C5
HallC3×C11⋊C5 ⋊ C22×C17
HallC2×C3×D11 ⋊ C5×C17
HallC11⋊C5 ⋊ C22×C3×C17
HallC2×D11 ⋊ C3×C5×C17
HallC3×C11 ⋊ C22×C5×C17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C22×C3×C5×C17
FrattiniC1G
Fitting, socleC2×C3×C11×C17C2×C5
LCSG ▷ C11
UCSC1 ◁ C2×C3×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1122 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C9×C17×AGL(1,𝔽11), C3×D3×C17×AGL(1,𝔽11), C2×C32×C17×AGL(1,𝔽11), …
maximal normal subgroup ofC2×C9×C17×AGL(1,𝔽11), C2×C32×C17×AGL(1,𝔽11)
maximal quotient ofC2×C9×C17×AGL(1,𝔽11), C3×D3×C17×AGL(1,𝔽11), C2×C32×C17×AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 38);