Finite Group Databasebeta

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C5×C11×A4×C19⋊C3 #49178627

order37620
automorphism?
homologyAbelianization (H1) = C32×C5×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC5×C11×A4×C19⋊C3
unambiguous semidirect product(C22×C19⋊C3)⋊(C3×C5×C11)
unambiguous semidirect product(A4×C19)⋊(C3×C5×C11)
unambiguous semidirect product(C22⋊(C19⋊C3))⋊(C3×C5×C11)
unambiguous semidirect product(C22×C5×C19⋊C3)⋊(C3×C11)
unambiguous semidirect product(C5×A4×C19)⋊(C3×C11)
unambiguous semidirect product(C5×C22⋊(C19⋊C3))⋊(C3×C11)
unambiguous semidirect product(C5×C11×C22⋊(C19⋊C3))⋊C3
unambiguous semidirect product(C5×C11×A4×C19)⋊C3
unambiguous semidirect product(C22×C5×C11×C19⋊C3)⋊C3

Splittings

Fitting, socle, HallC22×C5×C11×C19 ⋊ C32
derived, HallC22×C19 ⋊ C32×C5×C11
HallC5×C11×C19 ⋊ C3×A4
HallC22×C11×C19 ⋊ C32×C5
HallC22×C5×C19 ⋊ C32×C11
HallC22×C5×C11 ⋊ C3×C19⋊C3
HallC11×C19 ⋊ C3×C5×A4
HallC5×C19 ⋊ C3×C11×A4
HallC22×C11 ⋊ C3×C5×C19⋊C3
HallC22×C5 ⋊ C3×C11×C19⋊C3
SylowC19 ⋊ C3×C5×C11×A4
SylowC22 ⋊ C3×C5×C11×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC5×C11A4×C19⋊C3
commutator, cosocle, hypocenterC22×C19C32×C5×C11
FrattiniC1G
Fitting, socleC22×C5×C11×C19C32
LCSG ▷ C22×C19
UCSC1 ◁ C5×C11

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4180

Conjugacy classes & character table

1980 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 336);