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C3×C5×ΓL(1,𝔽8)⋊AGL(1,𝔽11) #46831535

order34650
automorphism?
homologyAbelianization (H1) = C2×C32×C52 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×C5×ΓL(1,𝔽8)⋊AGL(1,𝔽11)
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×C5×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C3×C5×AGL(1,𝔽7))
unambiguous semidirect product(C11⋊AGL(1,𝔽7))⋊(C3×C52)
unambiguous semidirect product(C7⋊AGL(1,𝔽11))⋊(C32×C5)
unambiguous semidirect product(C3×C11⋊AGL(1,𝔽7))⋊C52
unambiguous semidirect product(C3×C7⋊AGL(1,𝔽11))⋊(C3×C5)
unambiguous semidirect product(C5×C11⋊AGL(1,𝔽7))⋊(C3×C5)
unambiguous semidirect product(C5×C7⋊AGL(1,𝔽11))⋊C32
unambiguous semidirect product(C3×C5×C11⋊AGL(1,𝔽7))⋊C5
unambiguous semidirect product(C3×C5×C7⋊AGL(1,𝔽11))⋊C3

Splittings

Fitting, socleC3×C5×C7×C11 ⋊ C2×C3×C5
derived, HallC7×C11 ⋊ C2×C32×C52
HallC3×C5×ΓL(1,𝔽8)×C11⋊C5 ⋊ C2
HallC5×C7⋊AGL(1,𝔽11) ⋊ C32
HallC5×C7×C11⋊C5 ⋊ C2×C32
HallC3×C11⋊AGL(1,𝔽7) ⋊ C52
HallC3×C11×ΓL(1,𝔽8) ⋊ C2×C52
HallC5×C11⋊C5 ⋊ C3×AGL(1,𝔽7)
HallD77 ⋊ C32×C52
HallC3×ΓL(1,𝔽8) ⋊ C5×AGL(1,𝔽11)
SylowC11 ⋊ C3×C52×AGL(1,𝔽7)
SylowC7 ⋊ C32×C5×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC3×C5ΓL(1,𝔽8)⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC7×C11C2×C32×C52
FrattiniC1G
Fitting, socleC3×C5×C7×C11C2×C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C3×C5

384 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 128 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 178);