Finite Group Databasebeta

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C5×C19⋊C3×C121 #46828432

order34485
automorphism?
homologyAbelianization (H1) = C3×C5×C121 · Schur multiplier (H2) = C1

Aliases

direct productC5×C19⋊C3×C121
unambiguous semidirect productC19⋊(C3×C5×C121)
unambiguous semidirect product(C5×C19)⋊(C3×C121)
unambiguous semidirect product(C5×C19×C121)⋊C3

Splittings

Fitting, HallC5×C19×C121 ⋊ C3
derived, SylowC19 ⋊ C3×C5×C121
HallC19×C121 ⋊ C3×C5
HallC5×C19 ⋊ C3×C121

Subgroups

subgroupG/H
center, hypercenterC5×C121C19⋊C3
commutator, hypocenterC19C3×C5×C121
FrattiniC11C5×C11×C19⋊C3
FittingC5×C19×C121C3
socleC5×C11×C19C3×C11
prime radicalC5×C11×C19⋊C3C11
cosocleC11×C19C3×C5×C11
LCSG ▷ C19
UCSC1 ◁ C5×C121

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11495

Conjugacy classes & character table

5445 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34485, 3);