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C5×C11×AGL(1,𝔽13) #22575086

order8580
isoclinismisoclinic class of AGL(1,𝔽13)
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×AGL(1,𝔽13)
unambiguous semidirect product#261⋊(C3×C5×C11)
unambiguous semidirect product(C5×#261)⋊(C3×C11)
unambiguous semidirect product(C5×C11×#261)⋊C3

Splittings

Fitting, socle, HallC5×C11×C13 ⋊ C3×C4
derived, SylowC13 ⋊ C3×C4×C5×C11
HallC5×C11×#261 ⋊ C3
HallC5×C11×C13⋊C3 ⋊ C4
HallC11×#261 ⋊ C3×C5
HallC11×C13⋊C3 ⋊ C4×C5
HallC5×#261 ⋊ C3×C11
HallC5×C13⋊C3 ⋊ C4×C11
HallC11×C13 ⋊ C3×C4×C5
HallC5×C13 ⋊ C3×C4×C11
Hall#261 ⋊ C3×C5×C11
HallC13⋊C3 ⋊ C4×C5×C11

Subgroups

subgroupG/H
center, hypercenterC5×C11AGL(1,𝔽13)
commutator, hypocenterC13C3×C4×C5×C11
FrattiniC1G
Fitting, socleC5×C11×C13C3×C4
LCSG ▷ C13
UCSC1 ◁ C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

715 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×C11×AGL(1,𝔽13), C5×C11×C3⋊AGL(1,𝔽13)
maximal normal subgroup ofC3×C5×C11×AGL(1,𝔽13)
maximal quotient ofC5×C11×#261⋊C9, C3×C5×C11×AGL(1,𝔽13), C5×C11×C3⋊AGL(1,𝔽13)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 58);