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C3×ΓL(1,𝔽8)⋊(D11⋊C25) #46831395

order34650
automorphism?
homologyAbelianization (H1) = C2×C32×C25 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)⋊(D11⋊C25)
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×D11⋊C25)
unambiguous semidirect product(C11⋊C25)⋊(C3×AGL(1,𝔽7))
unambiguous semidirect product(C11⋊AGL(1,𝔽7))⋊(C3×C25)
unambiguous semidirect product(C3×C11⋊AGL(1,𝔽7))⋊C25
unambiguous semidirect product(C7⋊(D11⋊C25))⋊C32
unambiguous semidirect product(C3×C7⋊(D11⋊C25))⋊C3

Splittings

derived, HallC7×C11 ⋊ C2×C32×C25
HallC3×ΓL(1,𝔽8)×C11⋊C25 ⋊ C2
HallC7⋊(D11⋊C25) ⋊ C32
HallC7×C11⋊C25 ⋊ C2×C32
HallC3×C11⋊AGL(1,𝔽7) ⋊ C25
HallC3×C11×ΓL(1,𝔽8) ⋊ C2×C25
HallC11⋊C25 ⋊ C3×AGL(1,𝔽7)
HallD77 ⋊ C32×C25
HallC3×ΓL(1,𝔽8) ⋊ D11⋊C25
SylowC11 ⋊ C3×C25×AGL(1,𝔽7)
SylowC7 ⋊ C32×D11⋊C25

Subgroups

subgroupG/H
center, hypercenterC3×C5ΓL(1,𝔽8)⋊AGL(1,𝔽11)
commutator, hypocenterC7×C11C2×C32×C25
FrattiniC5C3×ΓL(1,𝔽8)⋊AGL(1,𝔽11)
Fitting, socleC3×C5×C7×C11C2×C3×C5
prime radicalC3×C5×C11⋊AGL(1,𝔽7)C5
cosocleC5×C7×C11C2×C32×C5
LCSG ▷ C7×C11
UCSC1 ◁ C3×C5

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5775

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, 38);