Finite Group Databasebeta

← Prev (#49178373) Next (#49178375) →

C9×D5×C11×D19 #49178374

order37620
automorphism?
homologyAbelianization (H1) = C22×C9×C11 · Schur multiplier (H2) = C2

Aliases

direct productC9×D5×C11×D19

Splittings

Fitting, HallC5×C9×C11×C19 ⋊ C22
derived, HallC5×C19 ⋊ C22×C9×C11
HallC9×C11×C19 ⋊ C2×D5
HallC5×C11×C19 ⋊ C22×C9
HallC5×C9×C19 ⋊ C22×C11
HallC5×C9×C11 ⋊ C2×D19
HallC11×C19 ⋊ C2×C9×D5
HallC9×C19 ⋊ C2×D5×C11
HallC5×C11 ⋊ C2×C9×D19
HallC5×C9 ⋊ C2×C11×D19
SylowC19 ⋊ C2×C9×D5×C11
SylowC5 ⋊ C2×C9×C11×D19

Subgroups

subgroupG/H
center, hypercenterC9×C11D5×D19
commutator, hypocenterC5×C19C22×C9×C11
FrattiniC3C3×D5×C11×D19
FittingC5×C9×C11×C19C22
socleC3×C5×C11×C19C22×C3
prime radicalC3×D5×C11×D19C3
cosocleC3×C5×C19C22×C3×C11
LCSG ▷ C5×C19
UCSC1 ◁ C9×C11

120 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 60 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

4356 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 83);