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C3×C11⋊C5×C5⋊AGL(1,𝔽7) #46831539

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

Aliases

direct productC3×C11⋊C5×C5⋊AGL(1,𝔽7)
unambiguous semidirect productC5⋊(C3×AGL(1,𝔽7)×C11⋊C5)
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×D5×C11⋊C5)
unambiguous semidirect productD35⋊(C32×C11⋊C5)
unambiguous semidirect product(C3×D35)⋊(C3×C11⋊C5)
unambiguous semidirect product(C11×C5⋊AGL(1,𝔽7))⋊(C3×C5)
unambiguous semidirect product(C11⋊C5×D35)⋊C32
unambiguous semidirect product(C3×C11×C5⋊AGL(1,𝔽7))⋊C5
unambiguous semidirect product(C3×C11⋊C5×D35)⋊C3

Splittings

Fitting, socleC3×C5×C7×C11 ⋊ C2×C3×C5
derivedC5×C7×C11 ⋊ C2×C32×C5
HallC3×C5×ΓL(1,𝔽8)×C11⋊C5 ⋊ C2
HallC11⋊C5×D35 ⋊ C32
HallC5×C7×C11⋊C5 ⋊ C2×C32
HallC3×C11×ΓL(1,𝔽8) ⋊ C5×D5
HallC5×C11⋊C5 ⋊ C3×AGL(1,𝔽7)
HallC7×C11 ⋊ C32×C5×D5
HallC3×ΓL(1,𝔽8) ⋊ D5×C11⋊C5
SylowC11 ⋊ C3×C5×C5⋊AGL(1,𝔽7)
SylowC7 ⋊ C32×D5×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC3C11⋊C5×C5⋊AGL(1,𝔽7)
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 66 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 66 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 182);