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AGL(1,𝔽103) #24901902

order10506
automorphism?
homologyAbelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1

Aliases

affine general linearAGL(1,𝔽103)
unambiguous semidirect product(D103⋊C3)⋊C17
unambiguous semidirect product(D103⋊C17)⋊C3
unambiguous semidirect product((C103⋊C3)⋊C17)⋊C2

Splittings

Fitting, socle, derived, SylowC103 ⋊ C2×C3×C17
Hall(C103⋊C3)⋊C17 ⋊ C2
HallD103⋊C17 ⋊ C3
HallC103⋊C17 ⋊ C2×C3
HallD103⋊C3 ⋊ C17
HallC103⋊C3 ⋊ C2×C17
HallD103 ⋊ C3×C17

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC103C2×C3×C17
LCSG ▷ C103
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,17,103|d^a=d^102,d^b=d^56,d^c=d^72

Conjugacy classes & character table

103 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽103), C3×AGL(1,𝔽103), C3⋊AGL(1,𝔽103)
maximal normal subgroup ofC2×AGL(1,𝔽103), C3×AGL(1,𝔽103)
maximal quotient of((C103⋊C3)⋊C4)⋊C17, C2×AGL(1,𝔽103), (D103⋊C9)⋊C17, …
automorphism group ofD103
holomorph ofC103

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10506, 18);