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C2×C3×ΓL(1,𝔽8)×C11⋊C25 #46831402

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

Aliases

direct productC2×C3×ΓL(1,𝔽8)×C11⋊C25
unambiguous semidirect product(C2×C7)⋊(C32×C11⋊C25)
unambiguous semidirect product(C2×C11)⋊(C3×ΓL(1,𝔽8)×C25)
unambiguous semidirect product(C2×C3×C7)⋊(C3×C11⋊C25)
unambiguous semidirect product(C2×C3×C11)⋊(ΓL(1,𝔽8)×C25)
unambiguous semidirect product(C2×C11×ΓL(1,𝔽8))⋊(C3×C25)
unambiguous semidirect product(C2×C3×C11×ΓL(1,𝔽8))⋊C25
unambiguous semidirect product(C2×C7×C11⋊C25)⋊C32
unambiguous semidirect product(C2×C3×C7×C11⋊C25)⋊C3

Splittings

derived, HallC7×C11 ⋊ C2×C32×C25
HallC2×C7×C11⋊C25 ⋊ C32
HallC7×C11⋊C25 ⋊ C2×C32
HallC2×C3×C11×ΓL(1,𝔽8) ⋊ C25
HallC3×C11×ΓL(1,𝔽8) ⋊ C2×C25
HallC2×C7×C11 ⋊ C32×C25
HallC2×C11 ⋊ C3×ΓL(1,𝔽8)×C25
HallC2×C7 ⋊ C32×C11⋊C25
SylowC11 ⋊ C2×C3×ΓL(1,𝔽8)×C25
SylowC7 ⋊ C2×C32×C11⋊C25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5ΓL(1,𝔽8)×C11⋊C5
commutator, hypocenterC7×C11C2×C32×C25
FrattiniC5C2×C3×ΓL(1,𝔽8)×C11⋊C5
Fitting, socleC2×C3×C5×C7×C11C3×C5
prime radicalC2×C3×C5×C11×ΓL(1,𝔽8)C5
cosocleC5×C7×C11C2×C32×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3×C5

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11550

Conjugacy classes & character table

1050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 45);