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C3×ΓL(1,𝔽8)×C5⋊AGL(1,𝔽11) #46831540

order34650
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)×C5⋊AGL(1,𝔽11)
unambiguous semidirect productC5⋊(C3×ΓL(1,𝔽8)×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C3×D5×ΓL(1,𝔽8))
unambiguous semidirect productD55⋊(C3×C5×ΓL(1,𝔽8))
unambiguous semidirect product(C3×D55)⋊(C5×ΓL(1,𝔽8))
unambiguous semidirect product(ΓL(1,𝔽8)×D55)⋊(C3×C5)
unambiguous semidirect product(C7×C5⋊AGL(1,𝔽11))⋊C32
unambiguous semidirect product(C3×ΓL(1,𝔽8)×D55)⋊C5
unambiguous semidirect product(C3×C7×C5⋊AGL(1,𝔽11))⋊C3

Splittings

Fitting, socleC3×C5×C7×C11 ⋊ C2×C3×C5
derivedC5×C7×C11 ⋊ C2×C32×C5
HallC3×C5×ΓL(1,𝔽8)×C11⋊C5 ⋊ C2
HallC7×C5⋊AGL(1,𝔽11) ⋊ C32
HallC5×C7×C11⋊C5 ⋊ C2×C32
HallC3×C11×ΓL(1,𝔽8) ⋊ C5×D5
HallC5×C11⋊C5 ⋊ C2×C3×ΓL(1,𝔽8)
HallC7×C11 ⋊ C32×C5×D5
SylowC11 ⋊ C3×C5×D5×ΓL(1,𝔽8)
SylowC7 ⋊ C32×C5⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC3ΓL(1,𝔽8)×C5⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC5×C7×C11C2×C32×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C11C2×C3×C5
LCSG ▷ C5×C7×C11
UCSC1 ◁ C3

240 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1155

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 183);