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C59×C3⋊AGL(1,𝔽11) #34085702

order19470
automorphism?
homologyAbelianization (H1) = C2×C5×C59 · Schur multiplier (H2) = C1

Aliases

direct productC59×C3⋊AGL(1,𝔽11)
unambiguous semidirect productC3⋊(C59×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(D3×C59)
unambiguous semidirect productD33⋊(C5×C59)
unambiguous semidirect product(C59×D33)⋊C5

Splittings

Fitting, socle, HallC3×C11×C59 ⋊ C2×C5
derived, HallC3×C11 ⋊ C2×C5×C59
HallC3×C11⋊C5×C59 ⋊ C2
HallC59×D33 ⋊ C5
HallC11⋊C5×C59 ⋊ D3
HallC11×C59 ⋊ C5×D3
HallC3×C59 ⋊ AGL(1,𝔽11)
HallC3×C11⋊C5 ⋊ C2×C59
HallD33 ⋊ C5×C59
HallC11⋊C5 ⋊ D3×C59
SylowC11 ⋊ C5×D3×C59
SylowC3 ⋊ C59×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC59C3⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC3×C11C2×C5×C59
FrattiniC1G
Fitting, socleC3×C11×C59C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C59

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1947

Conjugacy classes & character table

1062 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19470, 23);