Finite Group Databasebeta

← Prev (#46797973) Next (#46797975) →

C73×C11⋊AGL(1,𝔽7) #46797974

order33726
automorphism?
homologyAbelianization (H1) = C2×C3×C73 · Schur multiplier (H2) = C1

Aliases

direct productC73×C11⋊AGL(1,𝔽7)
unambiguous semidirect productC11⋊(AGL(1,𝔽7)×C73)
unambiguous semidirect productΓL(1,𝔽8)⋊(D11×C73)
unambiguous semidirect productD77⋊(C3×C73)

Splittings

Fitting, socle, HallC7×C11×C73 ⋊ C2×C3
derived, HallC7×C11 ⋊ C2×C3×C73
HallC11×ΓL(1,𝔽8)×C73 ⋊ C2
HallC73×D77 ⋊ C3
HallΓL(1,𝔽8)×C73 ⋊ D11
HallC11×C73 ⋊ AGL(1,𝔽7)
HallC7×C73 ⋊ C3×D11
HallC11×ΓL(1,𝔽8) ⋊ C2×C73
HallD77 ⋊ C3×C73
HallΓL(1,𝔽8) ⋊ D11×C73
SylowC11 ⋊ AGL(1,𝔽7)×C73
SylowC7 ⋊ C3×D11×C73

Subgroups

subgroupG/H
center, hypercenterC73C11⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC7×C11C2×C3×C73
FrattiniC1G
Fitting, socleC7×C11×C73C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C73

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5621

Conjugacy classes & character table

2336 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33726, 42);