Finite Group Databasebeta

← Prev (#34037815) Next (#34037817) →

C9×C11×D95 #34037816

order18810
automorphism?
homologyAbelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC9×C11×D95
unambiguous semidirect productC5⋊(C9×C11×D19)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC9×C11D95
commutator, hypocenterC5×C19C2×C9×C11
FrattiniC3C3×C11×D95
FittingC5×C9×C11×C19C2
socleC3×C5×C11×C19C2×C3
prime radicalC3×C11×D95C3
cosocleC3×C5×C19C2×C3×C11
LCSG ▷ C5×C19
UCSC1 ◁ C9×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9405

Conjugacy classes & character table

4851 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×D5×C11×D19, C9×D11×D95, C9×D55⋊D19, …
maximal normal subgroup ofC9×D5×C11×D19, C9×D11×D95, C9×D55⋊D19, …
maximal quotient ofC9×C11×Dic95, C2×C9×C11×D95

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 9);