Finite Group Databasebeta

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C3×C5⋊(C19⋊AGL(1,𝔽11)) #44535477

order31350
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5⋊(C19⋊AGL(1,𝔽11))
unambiguous semidirect productC5⋊(C3×C19⋊AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C3×D95)
unambiguous semidirect product(C3×D1045)⋊C5

Splittings

Fitting, socleC3×C5×C11×C19 ⋊ C2×C5
derivedC5×C11×C19 ⋊ C2×C3×C5
HallC3×C5×C19×C11⋊C5 ⋊ C2
HallC5×C19×C11⋊C5 ⋊ C2×C3
HallC3×C5×C11⋊C5 ⋊ D19
HallC3×C11×C19 ⋊ C5×D5
HallC5×C11⋊C5 ⋊ C3×D19
HallC11×C19 ⋊ C3×C5×D5
HallC3×C19 ⋊ C5⋊AGL(1,𝔽11)
HallC3×C11 ⋊ C5×D95
SylowC19 ⋊ C3×C5⋊AGL(1,𝔽11)
SylowC11 ⋊ C3×C5×D95

Subgroups

subgroupG/H
center, hypercenterC3C5⋊(C19⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC5×C11×C19C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C19C2×C5
LCSG ▷ C5×C11×C19
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3135

Conjugacy classes & character table

1020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 50);