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D3×C17×AGL(1,𝔽11) #26014355

order11220
automorphism?
homologyAbelianization (H1) = C22×C5×C17 · Schur multiplier (H2) = C2

Aliases

direct productD3×C17×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×D3×C17)
unambiguous semidirect product(D3×D11)⋊(C5×C17)
unambiguous semidirect product(C3×AGL(1,𝔽11))⋊(C2×C17)
unambiguous semidirect product(D3×C11⋊C5)⋊(C2×C17)
unambiguous semidirect product(C3⋊AGL(1,𝔽11))⋊(C2×C17)
unambiguous semidirect product(D3×C17×D11)⋊C5

Splittings

Fitting, socle, HallC3×C11×C17 ⋊ C22×C5
derived, HallC3×C11 ⋊ C22×C5×C17
HallC3×C17×C11⋊C5 ⋊ C22
HallD3×C17×D11 ⋊ C5
HallC17×C11⋊C5 ⋊ C2×D3
HallC11×C17 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C22×C17
HallD3×D11 ⋊ C5×C17
HallC11⋊C5 ⋊ C2×D3×C17
HallC3×C17 ⋊ C2×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×D3×C17
SylowC3 ⋊ C2×C17×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC17D3×AGL(1,𝔽11)
commutator, cosocle, hypocenterC3×C11C22×C5×C17
FrattiniC1G
Fitting, socleC3×C11×C17C22×C5
LCSG ▷ C3×C11
UCSC1 ◁ C17

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

561 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC17×D9×AGL(1,𝔽11), C3×D3×C17×AGL(1,𝔽11), D3×C17×C3⋊AGL(1,𝔽11), …
maximal normal subgroup ofC3×D3×C17×AGL(1,𝔽11)
maximal quotient ofC17×D9×AGL(1,𝔽11), C3×D3×C17×AGL(1,𝔽11), D3×C17×C3⋊AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 31);