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D13⋊C3×AGL(1,𝔽11) #22575067

order8580
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productD13⋊C3×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×D13⋊C3)
unambiguous semidirect productD13⋊(C3×AGL(1,𝔽11))
unambiguous semidirect product(D11×D13⋊C3)⋊C5
unambiguous semidirect product(D13×AGL(1,𝔽11))⋊C3
unambiguous semidirect product(C11⋊C5×D13⋊C3)⋊C2
unambiguous semidirect product(C13⋊C3×AGL(1,𝔽11))⋊C2
unambiguous semidirect product((C13⋊C3)⋊AGL(1,𝔽11))⋊C2

Splittings

Fitting, socle, derived, HallC11×C13 ⋊ C22×C3×C5
HallD13×AGL(1,𝔽11) ⋊ C3
HallC13⋊C3×C11⋊C5 ⋊ C22
HallD11×D13⋊C3 ⋊ C5
HallC13×C11⋊C5 ⋊ C22×C3
HallD11×D13 ⋊ C3×C5
HallC11×C13⋊C3 ⋊ C22×C5
HallC11⋊C5 ⋊ C2×D13⋊C3
HallC13⋊C3 ⋊ C2×AGL(1,𝔽11)
SylowC13 ⋊ C2×C3×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×D13⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC11×C13C22×C3×C5
LCSG ▷ C11×C13
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D13⋊C3×AGL(1,𝔽11), D13⋊C3×C3⋊AGL(1,𝔽11), AGL(1,𝔽11)×C3⋊(D13⋊C3), …
maximal normal subgroup ofC3×D13⋊C3×AGL(1,𝔽11), AGL(1,𝔽11)×AGL(1,𝔽13)
maximal quotient ofAGL(1,𝔽11)×D13⋊C9, C3×D13⋊C3×AGL(1,𝔽11), D13⋊C3×C3⋊AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 39);