Finite Group Databasebeta

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C3×C11×C17×C19⋊C3 #44544267

order31977
automorphism?
homologyAbelianization (H1) = C32×C11×C17 · Schur multiplier (H2) = C3

Aliases

direct productC3×C11×C17×C19⋊C3
unambiguous semidirect productC19⋊(C32×C11×C17)
unambiguous semidirect product(C3×C19)⋊(C3×C11×C17)
unambiguous semidirect product(C11×C19)⋊(C32×C17)
unambiguous semidirect product(C17×C19)⋊(C32×C11)
unambiguous semidirect product(C3×C11×C19)⋊(C3×C17)
unambiguous semidirect product(C3×C17×C19)⋊(C3×C11)
unambiguous semidirect product(C11×C17×C19)⋊C32
unambiguous semidirect product(C3×C11×C17×C19)⋊C3

Splittings

Fitting, socleC3×C11×C17×C19 ⋊ C3
derived, SylowC19 ⋊ C32×C11×C17
HallC11×C17×C19 ⋊ C32
HallC17×C19 ⋊ C32×C11
HallC11×C19 ⋊ C32×C17

Subgroups

subgroupG/H
center, hypercenterC3×C11×C17C19⋊C3
commutator, cosocle, hypocenterC19C32×C11×C17
FrattiniC1G
Fitting, socleC3×C11×C17×C19C3
LCSG ▷ C19
UCSC1 ◁ C3×C11×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10659

Conjugacy classes & character table

5049 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31977, 5);