Finite Group Databasebeta

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C3×C5×C11×C22⋊(C19⋊C3) #49178769

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

Aliases

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

Splittings

Fitting, socleC22×C3×C5×C11×C19 ⋊ C3
derived, HallC22×C19 ⋊ C32×C5×C11
HallC22×C5×C11×C19 ⋊ C32
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, hypercenterC3×C5×C11C22⋊(C19⋊C3)
commutator, cosocle, hypocenterC22×C19C32×C5×C11
FrattiniC1G
Fitting, socleC22×C3×C5×C11×C19C3
LCSG ▷ C22×C19
UCSC1 ◁ C3×C5×C11

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12540

Conjugacy classes & character table

4620 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 478);