Finite Group Databasebeta

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C19×C22⋊C9×C11⋊C5 #49178341

order37620
automorphism?
homologyAbelianization (H1) = C5×C9×C19 · Schur multiplier (H2) = C2

Aliases

direct productC19×C22⋊C9×C11⋊C5
unambiguous semidirect productC22⋊(C9×C19×C11⋊C5)
unambiguous semidirect productC11⋊(C5×C19×C22⋊C9)
unambiguous semidirect product(C22×C11⋊C5)⋊(C9×C19)
unambiguous semidirect product(C11×C22⋊C9)⋊(C5×C19)
unambiguous semidirect product(C11×C19×C22⋊C9)⋊C5

Splittings

derived, HallC22×C11 ⋊ C5×C9×C19
HallC11×C19×C22⋊C9 ⋊ C5
HallC22×C19×C11⋊C5 ⋊ C9
HallC22×C11×C19 ⋊ C5×C9
HallC11×C22⋊C9 ⋊ C5×C19
HallC22×C11⋊C5 ⋊ C9×C19
HallC11×C19 ⋊ C5×C22⋊C9
HallC22×C19 ⋊ C9×C11⋊C5
SylowC11 ⋊ C5×C19×C22⋊C9
SylowC22 ⋊ C9×C19×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC3×C19A4×C11⋊C5
commutator, hypocenterC22×C11C5×C9×C19
FrattiniC3A4×C19×C11⋊C5
Fitting, socleC22×C3×C11×C19C3×C5
prime radicalC22×C3×C19×C11⋊C5C3
cosocleC22×C3×C11C3×C5×C19
LCSG ▷ C22×C11
UCSC1 ◁ C3×C19

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3762

Conjugacy classes & character table

1596 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 50);