Finite Group Databasebeta

← Prev (#13182197) Next (#13182199) →

C16×AGL(1,𝔽11) #13182198

order1760
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C2×C5×C16 · Schur multiplier (H2) = C2

Aliases

direct productC16×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×C16)
unambiguous semidirect product(C16×D11)⋊C5

Splittings

FittingC11×C16 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C5×C16
HallC16×D11 ⋊ C5
HallC11⋊C5 ⋊ C2×C16

Subgroups

subgroupG/H
center, hypercenterC16AGL(1,𝔽11)
commutator, hypocenterC11C2×C5×C16
FrattiniC8C2×AGL(1,𝔽11)
FittingC11×C16C2×C5
socleC2×C11C2×C5×C8
prime radicalC2×AGL(1,𝔽11)C8
cosocleC8×C11C22×C5
LCSG ▷ C11
UCSC1 ◁ C16

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 176

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofM32×AGL(1,𝔽11), D16×AGL(1,𝔽11), SD32×AGL(1,𝔽11), …
maximal normal subgroup ofM32×AGL(1,𝔽11), D16×AGL(1,𝔽11), SD32×AGL(1,𝔽11)
maximal quotient ofAGL(1,𝔽11)×AGL(1,𝔽17)
automorphism group ofC17×D11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 7);