Finite Group Databasebeta

← Prev (#22575078) Next (#22575080) →

D3×C13⋊AGL(1,𝔽11) #22575079

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

Aliases

direct productD3×C13⋊AGL(1,𝔽11)
unambiguous semidirect product(D3×C13)⋊AGL(1,𝔽11)
unambiguous semidirect product(D3×C11⋊C5)⋊D13
unambiguous semidirect product(D3×D143)⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C13 ⋊ C22×C5
HallC3×C13×C11⋊C5 ⋊ C22
HallD3×D143 ⋊ 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 ⋊ D3×AGL(1,𝔽11)
SylowC11 ⋊ C5×D3×D13
SylowC3 ⋊ C2×C13⋊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

159 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD9×C13⋊AGL(1,𝔽11), D3×(C13⋊C3)⋊AGL(1,𝔽11), C3×D3×C13⋊AGL(1,𝔽11), …
maximal normal subgroup ofD3×(C13⋊C3)⋊AGL(1,𝔽11), C3×D3×C13⋊AGL(1,𝔽11)
maximal quotient ofD9×C13⋊AGL(1,𝔽11), C3×D3×C13⋊AGL(1,𝔽11), D3×C3⋊(C13⋊AGL(1,𝔽11)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 51);