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C5×D1881 #34037822

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

Aliases

direct productC5×D1881
unambiguous semidirect productC9⋊(C5×D209)
unambiguous semidirect productC19⋊(C5×D99)

Splittings

Fitting, HallC5×C9×C11×C19 ⋊ C2
derived, HallC9×C11×C19 ⋊ C2×C5
HallC5×C11×C19 ⋊ D9
HallC5×C9×C19 ⋊ D11
HallC5×C9×C11 ⋊ D19
HallC11×C19 ⋊ C5×D9
HallC9×C19 ⋊ C5×D11
HallC9×C11 ⋊ C5×D19
HallC5×C19 ⋊ D99
HallC5×C11 ⋊ D171
HallC5×C9 ⋊ D209
SylowC19 ⋊ C5×D99
SylowC11 ⋊ C5×D171
SylowC9 ⋊ C5×D209

Subgroups

subgroupG/H
center, hypercenterC5D1881
commutator, cosocle, hypocenterC9×C11×C19C2×C5
FrattiniC3C5×D627
FittingC5×C9×C11×C19C2
socleC3×C5×C11×C19D3
LCSG ▷ C9×C11×C19
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9405

Conjugacy classes & character table

4710 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D19×D99, C5×D11×D171, C5×D9×D209, …
maximal normal subgroup ofC5×D19×D99, C5×D11×D171, C5×D9×D209, …
maximal quotient ofC5×Dic1881, C2×C5×D1881

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 15);