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C5×(C11⋊C5)⋊(D19⋊C3) #44535465

order31350
automorphism?
homologyAbelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×(C11⋊C5)⋊(D19⋊C3)
unambiguous semidirect product(C11⋊C5)⋊(C5×D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(C5×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊(D19⋊C3))⋊C52
unambiguous semidirect product(C19⋊AGL(1,𝔽11))⋊(C3×C5)
unambiguous semidirect product(C5×C11⋊(D19⋊C3))⋊C5
unambiguous semidirect product(C5×C19⋊AGL(1,𝔽11))⋊C3

Splittings

Fitting, socleC5×C11×C19 ⋊ C2×C3×C5
derived, HallC11×C19 ⋊ C2×C3×C52
HallC5×C11⋊C5×C19⋊C3 ⋊ C2
HallC5×C19⋊AGL(1,𝔽11) ⋊ C3
HallC5×C19×C11⋊C5 ⋊ C2×C3
HallC11⋊(D19⋊C3) ⋊ C52
HallC11×C19⋊C3 ⋊ C2×C52
HallD209 ⋊ C3×C52
HallC5×C11⋊C5 ⋊ D19⋊C3
HallC19⋊C3 ⋊ C5×AGL(1,𝔽11)
SylowC19 ⋊ C3×C5×AGL(1,𝔽11)
SylowC11 ⋊ C52×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC5(C11⋊C5)⋊(D19⋊C3)
commutator, cosocle, hypocenterC11×C19C2×C3×C52
FrattiniC1G
Fitting, socleC5×C11×C19C2×C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C5

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1045

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 38);