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D3×C13×AGL(1,𝔽11) #22575077

order8580
automorphism?
homologyAbelianization (H1) = C22×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productD3×C13×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×D3×C13)
unambiguous semidirect product(D3×D11)⋊(C5×C13)
unambiguous semidirect product(C3×AGL(1,𝔽11))⋊(C2×C13)
unambiguous semidirect product(D3×C11⋊C5)⋊(C2×C13)
unambiguous semidirect product(C3⋊AGL(1,𝔽11))⋊(C2×C13)
unambiguous semidirect product(D3×C13×D11)⋊C5

Splittings

Fitting, socle, HallC3×C11×C13 ⋊ C22×C5
derived, HallC3×C11 ⋊ C22×C5×C13
HallC3×C13×C11⋊C5 ⋊ C22
HallD3×C13×D11 ⋊ C5
HallC13×C11⋊C5 ⋊ C2×D3
HallC3×C11⋊C5 ⋊ C22×C13
HallC11×C13 ⋊ C2×C5×D3
HallD3×D11 ⋊ C5×C13
HallC11⋊C5 ⋊ C2×D3×C13
HallC3×C13 ⋊ C2×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×D3×C13
SylowC3 ⋊ C2×C13×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC13D3×AGL(1,𝔽11)
commutator, hypocenterC3×C11C22×C5×C13
FrattiniC1G
Fitting, socleC3×C11×C13C22×C5
LCSG ▷ C3×C11
UCSC1 ◁ C13

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

429 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13×D9×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 ofC13×D9×AGL(1,𝔽11), C3×D3×C13×AGL(1,𝔽11), D3×C13×C3⋊AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 49);