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D51×AGL(1,𝔽11) #26014356

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

Aliases

direct productD51×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×D51)
unambiguous semidirect product(C3×AGL(1,𝔽11))⋊D17
unambiguous semidirect product(C17×AGL(1,𝔽11))⋊D3
unambiguous semidirect product(D11×D51)⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C17 ⋊ C22×C5
HallC3×C17×C11⋊C5 ⋊ C22
HallD11×D51 ⋊ C5
HallC17×C11⋊C5 ⋊ C2×D3
HallC11×C17 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C2×D17
HallC11⋊C5 ⋊ C2×D51
HallC3×C17 ⋊ C2×AGL(1,𝔽11)
HallC3×C11 ⋊ C2×C5×D17
SylowC17 ⋊ D3×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×D51
SylowC3 ⋊ D17×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

297 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×D153, C3×D51×AGL(1,𝔽11), D51×C3⋊AGL(1,𝔽11), …
maximal normal subgroup ofC3×D51×AGL(1,𝔽11)
maximal quotient ofAGL(1,𝔽11)×D153, C3×D51×AGL(1,𝔽11), D51×C3⋊AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 32);