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D13×C3⋊AGL(1,𝔽11) #22575076

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

Aliases

direct productD13×C3⋊AGL(1,𝔽11)
unambiguous semidirect product(C3×D13)⋊AGL(1,𝔽11)
unambiguous semidirect product(D13×C11⋊C5)⋊D3
unambiguous semidirect product(D13×D33)⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C13 ⋊ C22×C5
HallC3×C13×C11⋊C5 ⋊ C22
HallD13×D33 ⋊ C5
HallC13×C11⋊C5 ⋊ C2×D3
HallC3×C11⋊C5 ⋊ C2×D13
HallC11×C13 ⋊ C2×C5×D3
HallC11⋊C5 ⋊ D3×D13
HallC3×C13 ⋊ C2×AGL(1,𝔽11)
HallC3×C11 ⋊ C2×C5×D13
SylowC13 ⋊ C2×C3⋊AGL(1,𝔽11)
SylowC11 ⋊ C5×D3×D13
SylowC3 ⋊ D13×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C11×C13C22×C5
LCSG ▷ C3×C11×C13
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD13×C9⋊AGL(1,𝔽11), D13⋊C3×C3⋊AGL(1,𝔽11), C3×D13×C3⋊AGL(1,𝔽11), …
maximal normal subgroup ofD13⋊C3×C3⋊AGL(1,𝔽11), C3×D13×C3⋊AGL(1,𝔽11)
maximal quotient ofD13×C9⋊AGL(1,𝔽11), C3×D13×C3⋊AGL(1,𝔽11), D39⋊(C3⋊AGL(1,𝔽11)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 48);