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C5×C7×AGL(1,𝔽13) #19129708

order5460
isoclinismisoclinic class of AGL(1,𝔽13)
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×AGL(1,𝔽13)
unambiguous semidirect product#261⋊(C3×C5×C7)
unambiguous semidirect product(C5×#261)⋊(C3×C7)

Splittings

Fitting, socle, HallC5×C7×C13 ⋊ C3×C4
derived, SylowC13 ⋊ C3×C4×C5×C7
HallC5×C7×#261 ⋊ C3
HallC5×C7×C13⋊C3 ⋊ C4
HallC7×#261 ⋊ C3×C5
HallC7×C13⋊C3 ⋊ C4×C5
HallC5×#261 ⋊ C3×C7
HallC5×C13⋊C3 ⋊ C4×C7
HallC7×C13 ⋊ C3×C4×C5
HallC5×C13 ⋊ C3×C4×C7
Hall#261 ⋊ C3×C5×C7
HallC13⋊C3 ⋊ C4×C5×C7

Subgroups

subgroupG/H
center, hypercenterC5×C7AGL(1,𝔽13)
commutator, hypocenterC13C3×C4×C5×C7
FrattiniC1G
Fitting, socleC5×C7×C13C3×C4
LCSG ▷ C13
UCSC1 ◁ C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

455 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×ΓL(1,𝔽8)×AGL(1,𝔽13), C3×C5×C7×AGL(1,𝔽13), C5×C7×C3⋊AGL(1,𝔽13), …
maximal normal subgroup ofC5×ΓL(1,𝔽8)×AGL(1,𝔽13), C3×C5×C7×AGL(1,𝔽13), C7×C25×AGL(1,𝔽13), …
maximal quotient ofC5×C7×#261⋊C9, C3×C5×C7×AGL(1,𝔽13), C5×C7×C3⋊AGL(1,𝔽13), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 50);