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C41×AGL(1,𝔽13) #20264173

order6396
isoclinismisoclinic class of AGL(1,𝔽13)
automorphism?
homologyAbelianization (H1) = C3×C4×C41 · Schur multiplier (H2) = C1

Aliases

direct productC41×AGL(1,𝔽13)
unambiguous semidirect product#261⋊(C3×C41)
unambiguous semidirect product(C41×#261)⋊C3

Splittings

Fitting, socle, HallC13×C41 ⋊ C3×C4
derived, SylowC13 ⋊ C3×C4×C41
HallC41×#261 ⋊ C3
HallC13⋊C3×C41 ⋊ C4
Hall#261 ⋊ C3×C41
HallC13⋊C3 ⋊ C4×C41

Subgroups

subgroupG/H
center, hypercenterC41AGL(1,𝔽13)
commutator, hypocenterC13C3×C4×C41
FrattiniC1G
Fitting, socleC13×C41C3×C4
LCSG ▷ C13
UCSC1 ◁ C41

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

533 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C41×AGL(1,𝔽13), C41×C3⋊AGL(1,𝔽13), AGL(1,𝔽13)×C41⋊C5, …
maximal normal subgroup ofC3×C41×AGL(1,𝔽13), AGL(1,𝔽13)×C41⋊C5, C5×C41×AGL(1,𝔽13)
maximal quotient ofC41×#261⋊C9, C3×C41×AGL(1,𝔽13), C41×C3⋊AGL(1,𝔽13), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6396, 14);