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C3×C11⋊(ΓL(1,𝔽8)⋊D25) #46831418

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

Aliases

direct productC3×C11⋊(ΓL(1,𝔽8)⋊D25)
unambiguous semidirect productC11⋊(C3×ΓL(1,𝔽8)⋊D25)
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×D275)
unambiguous semidirect productC25⋊(C3×C11⋊AGL(1,𝔽7))
unambiguous semidirect productD1925⋊C32
unambiguous semidirect product(C3×D1925)⋊C3

Splittings

FittingC3×C7×C11×C25 ⋊ C2×C3
derived, HallC7×C11×C25 ⋊ C2×C32
HallC3×C11×ΓL(1,𝔽8)×C25 ⋊ C2
HallD1925 ⋊ C32
HallC3×ΓL(1,𝔽8)×C25 ⋊ D11
HallC3×C11×ΓL(1,𝔽8) ⋊ D25
HallC11×C25 ⋊ C3×AGL(1,𝔽7)
HallC7×C25 ⋊ C32×D11
HallC7×C11 ⋊ C32×D25
HallC3×ΓL(1,𝔽8) ⋊ D275
SylowC25 ⋊ C3×C11⋊AGL(1,𝔽7)
SylowC11 ⋊ C3×ΓL(1,𝔽8)⋊D25
SylowC7 ⋊ C32×D275

Subgroups

subgroupG/H
center, hypercenterC3C11⋊(ΓL(1,𝔽8)⋊D25)
commutator, cosocle, hypocenterC7×C11×C25C2×C32
FrattiniC5C3×C5⋊(C11⋊AGL(1,𝔽7))
FittingC3×C7×C11×C25C2×C3
socleC3×C5×C7×C11C3×D5
LCSG ▷ C7×C11×C25
UCSC1 ◁ C3

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5775

Conjugacy classes & character table

2076 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 61);