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AGL(1,𝔽31) #11745378

order930
isoclinismisoclinic class of AGL(1,𝔽31)
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

affine general linearAGL(1,𝔽31)
unambiguous semidirect product(D31⋊C3)⋊C5
unambiguous semidirect product(D31⋊C5)⋊C3
unambiguous semidirect product((C31⋊C3)⋊C5)⋊C2

Splittings

Fitting, socle, derived, SylowC31 ⋊ C2×C3×C5
Hall(C31⋊C3)⋊C5 ⋊ C2
HallD31⋊C5 ⋊ C3
HallD31⋊C3 ⋊ C5
HallΓL(1,𝔽32) ⋊ C2×C3
HallC31⋊C3 ⋊ C2×C5
HallD31 ⋊ C3×C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC31C2×C3×C5
LCSG ▷ C31
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31

Polycyclic presentation:

2,3,5,31|d^a=d^30,d^b=d^5,d^c=d^16

Conjugacy classes & character table

31 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽31), C3×AGL(1,𝔽31), C3⋊AGL(1,𝔽31), …
maximal normal subgroup ofC2×AGL(1,𝔽31), C3×AGL(1,𝔽31), C5×AGL(1,𝔽31), …
maximal quotient of((C31⋊C3)⋊C4)⋊C5, C2×AGL(1,𝔽31), (D31⋊C5)⋊C9, …
automorphism group ofD31, C31⋊C3, ΓL(1,𝔽32), …
holomorph ofC31

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(930, 1);