Finite Group Databasebeta

← Prev (#26014364) Next (#26014366) →

C2×C17×C3⋊AGL(1,𝔽11) #26014365

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

Aliases

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

Splittings

Fitting, socleC2×C3×C11×C17 ⋊ C2×C5
derived, HallC3×C11 ⋊ C22×C5×C17
HallC3×C17×C11⋊C5 ⋊ C22
HallC2×C17×D33 ⋊ C5
HallC17×C11⋊C5 ⋊ C2×D3
HallC3×C11×C17 ⋊ C22×C5
HallC11×C17 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C22×C17
HallC2×D33 ⋊ 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, hypercenterC2×C17C3⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC3×C11C22×C5×C17
FrattiniC1G
Fitting, socleC2×C3×C11×C17C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C2×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

612 conjugacy classes — view the full character table.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 41);