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C3×C11×ΓL(1,𝔽8)×C47 #45654663

order32571
automorphism?
homologyAbelianization (H1) = C32×C11×C47 · Schur multiplier (H2) = C3

Aliases

direct productC3×C11×ΓL(1,𝔽8)×C47
unambiguous semidirect productC7⋊(C32×C11×C47)
unambiguous semidirect product(C3×C7)⋊(C3×C11×C47)
unambiguous semidirect product(C7×C11)⋊(C32×C47)
unambiguous semidirect product(C3×C7×C11)⋊(C3×C47)
unambiguous semidirect product(C7×C47)⋊(C32×C11)
unambiguous semidirect product(C3×C7×C47)⋊(C3×C11)
unambiguous semidirect product(C7×C11×C47)⋊C32
unambiguous semidirect product(C3×C7×C11×C47)⋊C3

Splittings

Fitting, socleC3×C7×C11×C47 ⋊ C3
derived, SylowC7 ⋊ C32×C11×C47
HallC7×C11×C47 ⋊ C32
HallC7×C47 ⋊ C32×C11
HallC7×C11 ⋊ C32×C47

Subgroups

subgroupG/H
center, hypercenterC3×C11×C47ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C32×C11×C47
FrattiniC1G
Fitting, socleC3×C7×C11×C47C3
LCSG ▷ C7
UCSC1 ◁ C3×C11×C47

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10857

Conjugacy classes & character table

7755 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32571, 4);