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C11×AGL(1,𝔽7)×C52⋊C3 #46831550

order34650
automorphism?
homologyAbelianization (H1) = C2×C32×C11 · Schur multiplier (H2) = C3×C5

Aliases

direct productC11×AGL(1,𝔽7)×C52⋊C3
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C11×C52⋊C3)
unambiguous semidirect product(C52×AGL(1,𝔽7))⋊(C3×C11)
unambiguous semidirect product(D7×C52⋊C3)⋊(C3×C11)
unambiguous semidirect product(D7⋊(C52⋊C3))⋊(C3×C11)
unambiguous semidirect product(C52×C11×AGL(1,𝔽7))⋊C3
unambiguous semidirect product(C11×D7⋊(C52⋊C3))⋊C3
unambiguous semidirect product(C11×D7×C52⋊C3)⋊C3

Splittings

Fitting, socle, HallC52×C7×C11 ⋊ C2×C32
derived, HallC52×C7 ⋊ C2×C32×C11
HallC11×ΓL(1,𝔽8)×C52⋊C3 ⋊ C2
HallC52×C11×D7 ⋊ C32
HallΓL(1,𝔽8)×C52⋊C3 ⋊ C2×C11
HallC52×D7 ⋊ C32×C11
HallC52×C11 ⋊ C3×AGL(1,𝔽7)
HallC11×D7 ⋊ C3×C52⋊C3
HallC7×C11 ⋊ C2×C3×C52⋊C3
SylowC52 ⋊ C3×C11×AGL(1,𝔽7)
HallD7 ⋊ C3×C11×C52⋊C3
SylowC7 ⋊ C2×C3×C11×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC11AGL(1,𝔽7)×C52⋊C3
commutator, cosocle, hypocenterC52×C7C2×C32×C11
FrattiniC1G
Fitting, socleC52×C7×C11C2×C32
LCSG ▷ C52×C7
UCSC1 ◁ C11

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1155

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 193);