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C5×C9×D209 #34037814

order18810
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×D209

Splittings

Fitting, HallC5×C9×C11×C19 ⋊ C2
derived, HallC11×C19 ⋊ C2×C5×C9
HallC9×C11×C19 ⋊ C2×C5
HallC5×C11×C19 ⋊ C2×C9
HallC5×C9×C19 ⋊ D11
HallC5×C9×C11 ⋊ D19
HallC9×C19 ⋊ C5×D11
HallC9×C11 ⋊ C5×D19
HallC5×C19 ⋊ C9×D11
HallC5×C11 ⋊ C9×D19
SylowC19 ⋊ C5×C9×D11
SylowC11 ⋊ C5×C9×D19

Subgroups

subgroupG/H
center, hypercenterC5×C9D209
commutator, hypocenterC11×C19C2×C5×C9
FrattiniC3C3×C5×D209
FittingC5×C9×C11×C19C2
socleC3×C5×C11×C19C2×C3
prime radicalC3×C5×D209C3
cosocleC3×C11×C19C2×C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C5×C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9405

Conjugacy classes & character table

4770 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C9×D11×D19, C9×D5×D209, C9×D55⋊D19, …
maximal normal subgroup ofC5×C9×D11×D19, C9×D5×D209, C9×D55⋊D19, …
maximal quotient ofC5×C9×Dic209, C2×C5×C9×D209

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 7);