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C3×C11×C13×ΓL(1,𝔽8) #22583095

order9009
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C32×C11×C13 · Schur multiplier (H2) = C3

Aliases

direct productC3×C11×C13×ΓL(1,𝔽8)
unambiguous semidirect productC7⋊(C32×C11×C13)
unambiguous semidirect product(C3×C7)⋊(C3×C11×C13)
unambiguous semidirect product(C7×C11)⋊(C32×C13)
unambiguous semidirect product(C3×C7×C11)⋊(C3×C13)

Splittings

Fitting, socleC3×C7×C11×C13 ⋊ C3
derived, SylowC7 ⋊ C32×C11×C13
HallC7×C11×C13 ⋊ C32
HallC7×C13 ⋊ C32×C11
HallC7×C11 ⋊ C32×C13

Subgroups

subgroupG/H
center, hypercenterC3×C11×C13ΓL(1,𝔽8)
commutator, hypocenterC7C32×C11×C13
FrattiniC1G
Fitting, socleC3×C7×C11×C13C3
LCSG ▷ C7
UCSC1 ◁ C3×C11×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2145 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C11×C13×AGL(1,𝔽7), C3×C11×ΓL(1,𝔽8)⋊D13, C3×C13×C11⋊AGL(1,𝔽7), …
maximal normal subgroup ofC3×C11×C13×AGL(1,𝔽7), C3×C11×ΓL(1,𝔽8)⋊D13, C3×C13×C11⋊AGL(1,𝔽7), …
maximal quotient ofC2×C3×C11×C13×ΓL(1,𝔽8), C11×A4×C13×ΓL(1,𝔽8), C3×C11×C13×C22⋊ΓL(1,𝔽8)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9009, 10);