Finite Group Databasebeta

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D5×C11×D9×C19 #49178396

order37620
automorphism?
homologyAbelianization (H1) = C22×C11×C19 · Schur multiplier (H2) = C2

Aliases

direct productD5×C11×D9×C19
unambiguous semidirect product(C5×D9)⋊(C2×C11×C19)
unambiguous semidirect product(C9×D5)⋊(C2×C11×C19)
unambiguous semidirect productD45⋊(C2×C11×C19)

Splittings

Fitting, HallC5×C9×C11×C19 ⋊ C22
derived, HallC5×C9 ⋊ C22×C11×C19
HallC9×C11×C19 ⋊ C2×D5
HallC5×C11×C19 ⋊ C2×D9
HallC5×C9×C19 ⋊ C22×C11
HallC5×C9×C11 ⋊ C22×C19
HallC9×C19 ⋊ C2×D5×C11
HallC9×C11 ⋊ C2×D5×C19
HallC5×C19 ⋊ C2×C11×D9
HallC5×C11 ⋊ C2×D9×C19
SylowC9 ⋊ C2×D5×C11×C19
SylowC5 ⋊ C2×C11×D9×C19

Subgroups

subgroupG/H
center, hypercenterC11×C19D5×D9
commutator, cosocle, hypocenterC5×C9C22×C11×C19
FrattiniC3D3×D5×C11×C19
FittingC5×C9×C11×C19C22
socleC3×C5×C11×C19C2×D3
LCSG ▷ C5×C9
UCSC1 ◁ C11×C19

120 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9405

Conjugacy classes & character table

5016 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 105);