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C11⋊(D19⋊(C52⋊C3)) #44535491

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

Aliases

unambiguous semidirect productC11⋊(D19⋊(C52⋊C3))
unambiguous semidirect productD209⋊(C52⋊C3)

Splittings

Fitting, socle, derived, HallC52×C11×C19 ⋊ C2×C3
HallC11×C19⋊(C52⋊C3) ⋊ C2
HallC52×D209 ⋊ C3
HallC19⋊(C52⋊C3) ⋊ D11
HallC52×C19 ⋊ C3×D11
HallD209 ⋊ C52⋊C3
HallC52×C11 ⋊ D19⋊C3
HallC11×C19 ⋊ C2×C52⋊C3
SylowC52 ⋊ C11⋊(D19⋊C3)
SylowC19 ⋊ D11×C52⋊C3
SylowC11 ⋊ D19⋊(C52⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C11×C19C2×C3
LCSG ▷ C52×C11×C19
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3135

Polycyclic presentation:

2,3,5^2,11,19|e^a=e^10,f^a=f^18,c^b=cd^3,d^b=c^4d^3,f^b=f^7

Conjugacy classes & character table

902 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 64);