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D3×C7×AGL(1,𝔽11) #17987646

order4620
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productD3×C7×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×D3×C7)
unambiguous semidirect product(D3×D11)⋊(C5×C7)
unambiguous semidirect product(C3×AGL(1,𝔽11))⋊(C2×C7)
unambiguous semidirect product(D3×C11⋊C5)⋊(C2×C7)
unambiguous semidirect product(C3⋊AGL(1,𝔽11))⋊(C2×C7)
unambiguous semidirect product(D3×C7×D11)⋊C5

Splittings

Fitting, socle, HallC3×C7×C11 ⋊ C22×C5
derived, HallC3×C11 ⋊ C22×C5×C7
HallC3×C7×C11⋊C5 ⋊ C22
HallD3×C7×D11 ⋊ C5
HallC7×C11⋊C5 ⋊ C2×D3
HallC3×C11⋊C5 ⋊ C22×C7
HallD3×D11 ⋊ C5×C7
HallC7×C11 ⋊ C2×C5×D3
HallC11⋊C5 ⋊ C2×D3×C7
HallC3×C7 ⋊ C2×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×D3×C7
SylowC3 ⋊ C2×C7×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC7D3×AGL(1,𝔽11)
commutator, cosocle, hypocenterC3×C11C22×C5×C7
FrattiniC1G
Fitting, socleC3×C7×C11C22×C5
LCSG ▷ C3×C11
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 231

Conjugacy classes & character table

231 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×D9×AGL(1,𝔽11), D3×ΓL(1,𝔽8)×AGL(1,𝔽11), C3×D3×C7×AGL(1,𝔽11), …
maximal normal subgroup ofD3×ΓL(1,𝔽8)×AGL(1,𝔽11), C3×D3×C7×AGL(1,𝔽11), C5×D3×C7×AGL(1,𝔽11), …
maximal quotient ofC7×D9×AGL(1,𝔽11), C3×D3×C7×AGL(1,𝔽11), C7×C3⋊D3×AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4620, 43);