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C3×C5×C11×AGL(1,𝔽7) #20294170

order6930
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C11 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C11×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C32×C5×C11)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C3×C5×C11)
unambiguous semidirect product(C3×D7)⋊(C3×C5×C11)
unambiguous semidirect product(C5×D7)⋊(C32×C11)
unambiguous semidirect product(C3×C5×D7)⋊(C3×C11)
unambiguous semidirect product(C5×C11×D7)⋊C32
unambiguous semidirect product(C3×C5×C11×D7)⋊C3

Splittings

Fitting, socleC3×C5×C7×C11 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C32×C5×C11
HallC3×C5×C11×ΓL(1,𝔽8) ⋊ C2
HallC5×C11×D7 ⋊ C32
HallC3×C11×ΓL(1,𝔽8) ⋊ C2×C5
HallC5×C7×C11 ⋊ C2×C32
HallC3×C5×ΓL(1,𝔽8) ⋊ C2×C11
HallC11×D7 ⋊ C32×C5
HallC7×C11 ⋊ C2×C32×C5
HallC5×D7 ⋊ C32×C11
HallC3×ΓL(1,𝔽8) ⋊ C2×C5×C11
HallC5×C7 ⋊ C2×C32×C11
HallD7 ⋊ C32×C5×C11

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11AGL(1,𝔽7)
commutator, hypocenterC7C2×C32×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C7×C11C2×C3
LCSG ▷ C7
UCSC1 ◁ C3×C5×C11

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1155 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×D11×AGL(1,𝔽7), C3×D5×C11×AGL(1,𝔽7), C3×AGL(1,𝔽7)×D55, …
maximal normal subgroup ofC3×C5×D11×AGL(1,𝔽7), C3×D5×C11×AGL(1,𝔽7), C3×AGL(1,𝔽7)×D55, …
maximal quotient ofC3×C5×C11×ΓL(1,𝔽8)⋊C4, C2×C3×C5×C11×AGL(1,𝔽7), C3×C11×C25×AGL(1,𝔽7), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 57);