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C5×C7×C11×AGL(1,𝔽7) #30633526

order16170
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×C11×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×C5×C7×C11)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C5×C7×C11)
unambiguous semidirect product(C5×D7)⋊(C3×C7×C11)
unambiguous semidirect product(C5×C11×D7)⋊(C3×C7)

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C2×C3
derivedC7 ⋊ C2×C3×C5×C7×C11
HallC5×C7×C11×ΓL(1,𝔽8) ⋊ C2
HallC5×C7×C11×D7 ⋊ C3
HallC7×C11×ΓL(1,𝔽8) ⋊ C2×C5
HallC7×C11×D7 ⋊ C3×C5
HallC5×C7×ΓL(1,𝔽8) ⋊ C2×C11
HallC72×C11 ⋊ C2×C3×C5
HallC5×C7×D7 ⋊ C3×C11
HallC5×C72 ⋊ C2×C3×C11
HallC7×ΓL(1,𝔽8) ⋊ C2×C5×C11
HallC7×D7 ⋊ C3×C5×C11
SylowC72 ⋊ C2×C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC5×C7×C11AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C2×C3×C5×C7×C11
FrattiniC1G
Fitting, socleC5×C72×C11C2×C3
LCSG ▷ C7
UCSC1 ◁ C5×C7×C11

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

2695 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C7×D11×AGL(1,𝔽7), C5×C11×D7×AGL(1,𝔽7), C5×AGL(1,𝔽7)×D77, …
maximal normal subgroup ofC5×C7×D11×AGL(1,𝔽7), C5×C11×D7×AGL(1,𝔽7), C5×AGL(1,𝔽7)×D77, …
maximal quotient ofC5×C7×C11×ΓL(1,𝔽8)⋊C4, C2×C5×C7×C11×AGL(1,𝔽7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 71);