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C3×C7×C3⋊AGL(1,𝔽11) #20294162

order6930
isoclinismisoclinic class of C3⋊AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C3⋊AGL(1,𝔽11)
unambiguous semidirect productC3⋊(C3×C7×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C3×D3×C7)
unambiguous semidirect productD33⋊(C3×C5×C7)
unambiguous semidirect product(C3×D33)⋊(C5×C7)
unambiguous semidirect product(C3×C7×D33)⋊C5

Splittings

Fitting, socle, HallC32×C7×C11 ⋊ C2×C5
derivedC3×C11 ⋊ C2×C3×C5×C7
HallC32×C7×C11⋊C5 ⋊ C2
HallC3×C7×D33 ⋊ C5
HallC32×C11⋊C5 ⋊ C2×C7
HallC7×C11⋊C5 ⋊ C3×D3
HallC3×D33 ⋊ C5×C7
HallC32×C11 ⋊ C2×C5×C7
HallC7×C11 ⋊ C3×C5×D3
HallC32×C7 ⋊ AGL(1,𝔽11)
HallC11⋊C5 ⋊ C3×D3×C7
SylowC11 ⋊ C3×C5×D3×C7
SylowC32 ⋊ C7×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC3×C7C3⋊AGL(1,𝔽11)
commutator, hypocenterC3×C11C2×C3×C5×C7
FrattiniC1G
Fitting, socleC32×C7×C11C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C3×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

378 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D3×C7×AGL(1,𝔽11), C3×D7×C3⋊AGL(1,𝔽11), C3×D21⋊AGL(1,𝔽11), …
maximal normal subgroup ofC3×D3×C7×AGL(1,𝔽11), C3×D7×C3⋊AGL(1,𝔽11), C3×D21⋊AGL(1,𝔽11), …
maximal quotient ofC3×C7×C3⋊(Dic11⋊C5), C2×C3×C7×C3⋊AGL(1,𝔽11), C3×C7×C3⋊(D11⋊C25), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 49);