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C71×C3⋊AGL(1,𝔽11) #37552905

order23430
automorphism?
homologyAbelianization (H1) = C2×C5×C71 · Schur multiplier (H2) = C1

Aliases

direct productC71×C3⋊AGL(1,𝔽11)
unambiguous semidirect productC3⋊(C71×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(D3×C71)
unambiguous semidirect productD33⋊(C5×C71)

Splittings

Fitting, socle, HallC3×C11×C71 ⋊ C2×C5
derived, HallC3×C11 ⋊ C2×C5×C71
HallC3×C11⋊C5×C71 ⋊ C2
HallD33×C71 ⋊ C5
HallC11⋊C5×C71 ⋊ D3
HallC11×C71 ⋊ C5×D3
HallC3×C71 ⋊ AGL(1,𝔽11)
HallC3×C11⋊C5 ⋊ C2×C71
HallD33 ⋊ C5×C71
HallC11⋊C5 ⋊ D3×C71
SylowC11 ⋊ C5×D3×C71
SylowC3 ⋊ C71×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC71C3⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC3×C11C2×C5×C71
FrattiniC1G
Fitting, socleC3×C11×C71C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C71

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2343

Conjugacy classes & character table

1278 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23430, 54);