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C71×C11⋊AGL(1,𝔽7) #45659039

order32802
automorphism?
homologyAbelianization (H1) = C2×C3×C71 · Schur multiplier (H2) = C1

Aliases

direct productC71×C11⋊AGL(1,𝔽7)
unambiguous semidirect productC11⋊(AGL(1,𝔽7)×C71)
unambiguous semidirect productΓL(1,𝔽8)⋊(D11×C71)
unambiguous semidirect productD77⋊(C3×C71)
unambiguous semidirect product(C71×D77)⋊C3

Splittings

Fitting, socle, HallC7×C11×C71 ⋊ C2×C3
derived, HallC7×C11 ⋊ C2×C3×C71
HallC11×ΓL(1,𝔽8)×C71 ⋊ C2
HallC71×D77 ⋊ C3
HallΓL(1,𝔽8)×C71 ⋊ D11
HallC11×C71 ⋊ AGL(1,𝔽7)
HallC7×C71 ⋊ C3×D11
HallC11×ΓL(1,𝔽8) ⋊ C2×C71
HallD77 ⋊ C3×C71
HallΓL(1,𝔽8) ⋊ D11×C71
SylowC11 ⋊ AGL(1,𝔽7)×C71
SylowC7 ⋊ C3×D11×C71

Subgroups

subgroupG/H
center, hypercenterC71C11⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC7×C11C2×C3×C71
FrattiniC1G
Fitting, socleC7×C11×C71C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C71

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5467

Conjugacy classes & character table

2272 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32802, 31);