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C5×C11⋊AGL(1,𝔽13) #22575087

order8580
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC5×C11×C13 ⋊ C3×C4
derived, HallC11×C13 ⋊ C3×C4×C5
HallC5×C11⋊#261 ⋊ C3
HallC5×C11×C13⋊C3 ⋊ C4
HallC11⋊#261 ⋊ C3×C5
HallC11×C13⋊C3 ⋊ C4×C5
HallC5×C13⋊C3 ⋊ Dic11
HallC5×C13 ⋊ C3×Dic11
HallC5×C11 ⋊ AGL(1,𝔽13)
HallC13⋊C3 ⋊ C5×Dic11
SylowC13 ⋊ C3×C5×Dic11
SylowC11 ⋊ C5×AGL(1,𝔽13)

Subgroups

subgroupG/H
center, hypercenterC5C11⋊AGL(1,𝔽13)
commutator, hypocenterC11×C13C3×C4×C5
FrattiniC1G
Fitting, socleC5×C11×C13C3×C4
LCSG ▷ C11×C13
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

265 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×C11⋊AGL(1,𝔽13), C5×C3⋊(C11⋊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×C3⋊(C11⋊AGL(1,𝔽13))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 59);