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C5×C3⋊(C19⋊AGL(1,𝔽11)) #44535481

order31350
automorphism?
homologyAbelianization (H1) = C2×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×C3⋊(C19⋊AGL(1,𝔽11))
unambiguous semidirect productC3⋊(C5×C19⋊AGL(1,𝔽11))
unambiguous semidirect productC19⋊(C5×C3⋊AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C5×D57)
unambiguous semidirect productD627⋊C52
unambiguous semidirect product(C5×D627)⋊C5

Splittings

Fitting, socleC3×C5×C11×C19 ⋊ C2×C5
derived, HallC3×C11×C19 ⋊ C2×C52
HallC3×C5×C19×C11⋊C5 ⋊ C2
HallC5×C19×C11⋊C5 ⋊ D3
HallD627 ⋊ C52
HallC3×C5×C11⋊C5 ⋊ D19
HallC5×C11⋊C5 ⋊ D57
HallC11×C19 ⋊ C52×D3
HallC3×C19 ⋊ C5×AGL(1,𝔽11)
HallC3×C11 ⋊ C52×D19
SylowC19 ⋊ C5×C3⋊AGL(1,𝔽11)
SylowC11 ⋊ C52×D57
SylowC3 ⋊ C5×C19⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C19⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC3×C11×C19C2×C52
FrattiniC1G
Fitting, socleC3×C5×C11×C19C2×C5
LCSG ▷ C3×C11×C19
UCSC1 ◁ C5

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3135

Conjugacy classes & character table

1035 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 54);