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AGL(1,𝔽27) #10622065

order702
isoclinismisoclinic class of AGL(1,𝔽27)
automorphism?
homologyAbelianization (H1) = C2×C13 · Schur multiplier (H2) = C1

Aliases

affine general linearAGL(1,𝔽27)
unambiguous semidirect product(C3⋊(C3⋊D3))⋊C13
unambiguous semidirect product(C33⋊C13)⋊C2

Splittings

Fitting, socle, derived, SylowC33 ⋊ C2×C13
HallC33⋊C13 ⋊ C2
HallC3⋊(C3⋊D3) ⋊ C13

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC33C2×C13
LCSG ▷ C33
UCSC1

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 27

Polycyclic presentation:

2,13,3^3|c^a=c^2,d^a=d^2,e^a=e^2,c^b=d^2,d^b=e^2,e^b=ce^2

Conjugacy classes & character table

27 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽27), PGL(2,𝔽27), C13×AGL(1,𝔽27), …
maximal normal subgroup ofC2×AGL(1,𝔽27), C13×AGL(1,𝔽27), AΓL(1,𝔽27)
maximal quotient of(C3⋊(C3⋊Dic3))⋊C13, C2×AGL(1,𝔽27), C13×AGL(1,𝔽27)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(702, 47);