Finite Group Databasebeta

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C9×D5×D209 #49178378

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

Aliases

direct productC9×D5×D209
unambiguous semidirect product(D5×C11)⋊(C9×D19)

Splittings

Fitting, HallC5×C9×C11×C19 ⋊ C22
derived, HallC5×C11×C19 ⋊ C22×C9
HallC9×C11×C19 ⋊ C2×D5
HallC5×C9×C19 ⋊ C2×D11
HallC5×C9×C11 ⋊ C2×D19
HallC11×C19 ⋊ C2×C9×D5
HallC9×C19 ⋊ D5×D11
HallC9×C11 ⋊ D5×D19
HallC5×C19 ⋊ C2×C9×D11
HallC5×C11 ⋊ C2×C9×D19
HallC5×C9 ⋊ C2×D209
SylowC19 ⋊ C9×D5×D11
SylowC11 ⋊ C9×D5×D19
SylowC5 ⋊ C2×C9×D209

Subgroups

subgroupG/H
center, hypercenterC9D5×D209
commutator, hypocenterC5×C11×C19C22×C9
FrattiniC3C3×D5×D209
FittingC5×C9×C11×C19C22
socle, cosocleC3×C5×C11×C19C22×C3
prime radicalC3×D5×D209C3
LCSG ▷ C5×C11×C19
UCSC1 ◁ C9

120 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 48 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

3816 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 87);