Finite Group Databasebeta

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C19×C3⋊(C5⋊AGL(1,𝔽11)) #44535484

order31350
automorphism?
homologyAbelianization (H1) = C2×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×C3⋊(C5⋊AGL(1,𝔽11))
unambiguous semidirect productC3⋊(C19×C5⋊AGL(1,𝔽11))
unambiguous semidirect productC5⋊(C19×C3⋊AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C19×D15)
unambiguous semidirect productD165⋊(C5×C19)
unambiguous semidirect product(C19×D165)⋊C5

Splittings

Fitting, socleC3×C5×C11×C19 ⋊ C2×C5
derivedC3×C5×C11 ⋊ C2×C5×C19
HallC3×C5×C19×C11⋊C5 ⋊ C2
HallC5×C19×C11⋊C5 ⋊ D3
HallC3×C5×C11⋊C5 ⋊ C2×C19
HallC3×C11×C19 ⋊ C5×D5
HallC5×C11⋊C5 ⋊ D3×C19
HallC11×C19 ⋊ C5×D15
HallC3×C19 ⋊ C5⋊AGL(1,𝔽11)
HallC3×C11 ⋊ C5×D5×C19
SylowC11 ⋊ C5×C19×D15
SylowC3 ⋊ C19×C5⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC19C3⋊(C5⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC3×C5×C11C2×C5×C19
FrattiniC1G
Fitting, socleC3×C5×C11×C19C2×C5
LCSG ▷ C3×C5×C11
UCSC1 ◁ C19

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3135

Conjugacy classes & character table

1140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 57);