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D3×C17⋊AGL(1,𝔽11) #26014357

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

Aliases

direct productD3×C17⋊AGL(1,𝔽11)
unambiguous semidirect product(D3×C17)⋊AGL(1,𝔽11)
unambiguous semidirect product(D3×C11⋊C5)⋊D17
unambiguous semidirect product(D3×D187)⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C17 ⋊ C22×C5
HallC3×C17×C11⋊C5 ⋊ C22
HallD3×D187 ⋊ C5
HallC17×C11⋊C5 ⋊ C2×D3
HallC11×C17 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C2×D17
HallC11⋊C5 ⋊ D3×D17
HallC3×C17 ⋊ C2×AGL(1,𝔽11)
HallC3×C11 ⋊ C2×C5×D17
SylowC17 ⋊ D3×AGL(1,𝔽11)
SylowC11 ⋊ C5×D3×D17
SylowC3 ⋊ C2×C17⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C17C22×C5
LCSG ▷ C3×C11×C17
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

201 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD9×C17⋊AGL(1,𝔽11), C3×D3×C17⋊AGL(1,𝔽11), D3×C3⋊(C17⋊AGL(1,𝔽11)), …
maximal normal subgroup ofC3×D3×C17⋊AGL(1,𝔽11)
maximal quotient ofD9×C17⋊AGL(1,𝔽11), C3×D3×C17⋊AGL(1,𝔽11), D3×C3⋊(C17⋊AGL(1,𝔽11)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 33);