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C11⋊C5×AGL(1,𝔽13) #22575068

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

Aliases

direct productC11⋊C5×AGL(1,𝔽13)
unambiguous semidirect product#261⋊(C3×C11⋊C5)
unambiguous semidirect product(C11×AGL(1,𝔽13))⋊C5
unambiguous semidirect product(#261×C11⋊C5)⋊C3

Splittings

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

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC11×C13C3×C4×C5
LCSG ▷ C11×C13
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

91 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C11⋊C5×AGL(1,𝔽13), C11⋊C5×C3⋊AGL(1,𝔽13), AGL(1,𝔽11)×AGL(1,𝔽13)
maximal normal subgroup ofC3×C11⋊C5×AGL(1,𝔽13), AGL(1,𝔽11)×AGL(1,𝔽13)
maximal quotient ofC11⋊C5×#261⋊C9, C3×C11⋊C5×AGL(1,𝔽13), C11⋊C5×C3⋊AGL(1,𝔽13)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 40);