Finite Group Databasebeta

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C3×C11⋊C5×C22⋊(C19⋊C3) #49178570

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

Aliases

direct productC3×C11⋊C5×C22⋊(C19⋊C3)
unambiguous semidirect productC11⋊(C3×C5×C22⋊(C19⋊C3))
unambiguous semidirect product(C22×C3)⋊(C11⋊C5×C19⋊C3)
unambiguous semidirect product(C3×C11)⋊(C5×C22⋊(C19⋊C3))
unambiguous semidirect product(C3×C19)⋊(A4×C11⋊C5)
unambiguous semidirect product(C22×C3×C11⋊C5)⋊(C19⋊C3)
unambiguous semidirect product(C3×C19×C11⋊C5)⋊A4
unambiguous semidirect product(C3×C11×C22⋊(C19⋊C3))⋊C5

Splittings

Fitting, socleC22×C3×C11×C19 ⋊ C3×C5
derived, HallC22×C11×C19 ⋊ C32×C5
HallC3×C11×C22⋊(C19⋊C3) ⋊ C5
HallC22×C19×C11⋊C5 ⋊ C32
HallC19×C11⋊C5 ⋊ C3×A4
HallC22×C11⋊C5 ⋊ C3×C19⋊C3
HallC11×C19 ⋊ C3×C5×A4
HallC22×C19 ⋊ C32×C11⋊C5
HallC22×C11 ⋊ C3×C5×C19⋊C3
SylowC19 ⋊ C3×A4×C11⋊C5
SylowC11 ⋊ C3×C5×C22⋊(C19⋊C3)
SylowC22 ⋊ C3×C11⋊C5×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC3C11⋊C5×C22⋊(C19⋊C3)
commutator, cosocle, hypocenterC22×C11×C19C32×C5
FrattiniC1G
Fitting, socleC22×C3×C11×C19C3×C5
LCSG ▷ C22×C11×C19
UCSC1 ◁ C3

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2508

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 279);