Finite Group Databasebeta

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C22×C9×C19×C11⋊C5 #49178368

order37620
automorphism?
homologyAbelianization (H1) = C22×C5×C9×C19 · Schur multiplier (H2) = C2

Aliases

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

Splittings

Fitting, HallC22×C9×C11×C19 ⋊ C5
derived, SylowC11 ⋊ C22×C5×C9×C19
HallC9×C11×C19 ⋊ C22×C5
HallC22×C11×C19 ⋊ C5×C9
HallC22×C9×C11 ⋊ C5×C19
HallC11×C19 ⋊ C22×C5×C9
HallC9×C11 ⋊ C22×C5×C19
HallC22×C11 ⋊ C5×C9×C19

Subgroups

subgroupG/H
center, hypercenterC22×C9×C19C11⋊C5
commutator, hypocenterC11C22×C5×C9×C19
FrattiniC3C22×C3×C19×C11⋊C5
FittingC22×C9×C11×C19C5
socleC22×C3×C11×C19C3×C5
prime radicalC22×C3×C19×C11⋊C5C3
cosocleC3×C11C22×C3×C5×C19
LCSG ▷ C11
UCSC1 ◁ C22×C9×C19

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7524

Conjugacy classes & character table

4788 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 77);