Finite Group Databasebeta

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C19×D11×D45 #49178392

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

Aliases

direct productC19×D11×D45
unambiguous semidirect product(C5×D11)⋊(D9×C19)
unambiguous semidirect product(C9×D11)⋊(D5×C19)

Splittings

Fitting, HallC5×C9×C11×C19 ⋊ C22
derived, HallC5×C9×C11 ⋊ C22×C19
HallC9×C11×C19 ⋊ C2×D5
HallC5×C11×C19 ⋊ C2×D9
HallC5×C9×C19 ⋊ C2×D11
HallC11×C19 ⋊ C2×D45
HallC9×C19 ⋊ D5×D11
HallC9×C11 ⋊ C2×D5×C19
HallC5×C19 ⋊ D9×D11
HallC5×C11 ⋊ C2×D9×C19
HallC5×C9 ⋊ C2×C19×D11
SylowC11 ⋊ C2×C19×D45
SylowC9 ⋊ D5×C19×D11
SylowC5 ⋊ D9×C19×D11

Subgroups

subgroupG/H
center, hypercenterC19D11×D45
commutator, cosocle, hypocenterC5×C9×C11C22×C19
FrattiniC3C19×D11×D15
FittingC5×C9×C11×C19C22
socleC3×C5×C11×C19C2×D3
LCSG ▷ C5×C9×C11
UCSC1 ◁ C19

120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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

3192 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 101);