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C11×ΓL(1,𝔽8)⋊D71 #45659038

order32802
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×ΓL(1,𝔽8)⋊D71
unambiguous semidirect productΓL(1,𝔽8)⋊(C11×D71)
unambiguous semidirect productC71⋊(C11×AGL(1,𝔽7))
unambiguous semidirect productD497⋊(C3×C11)
unambiguous semidirect product(C11×D497)⋊C3

Splittings

Fitting, socle, HallC7×C11×C71 ⋊ C2×C3
derived, HallC7×C71 ⋊ C2×C3×C11
HallC11×ΓL(1,𝔽8)×C71 ⋊ C2
HallC11×D497 ⋊ C3
HallΓL(1,𝔽8)×C71 ⋊ C2×C11
HallD497 ⋊ C3×C11
HallC11×C71 ⋊ AGL(1,𝔽7)
HallC11×ΓL(1,𝔽8) ⋊ D71
HallC7×C11 ⋊ C3×D71
SylowC71 ⋊ C11×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C11×D71
SylowC7 ⋊ C3×C11×D71

Subgroups

subgroupG/H
center, hypercenterC11ΓL(1,𝔽8)⋊D71
commutator, cosocle, hypocenterC7×C71C2×C3×C11
FrattiniC1G
Fitting, socleC7×C11×C71C2×C3
LCSG ▷ C7×C71
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5467

Conjugacy classes & character table

2002 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32802, 30);