Finite Group Databasebeta

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C9×D5×C11×C19 #34037815

order18810
automorphism?
homologyAbelianization (H1) = C2×C9×C11×C19 · Schur multiplier (H2) = C1

Aliases

direct productC9×D5×C11×C19
unambiguous semidirect productC5⋊(C2×C9×C11×C19)

Splittings

Fitting, HallC5×C9×C11×C19 ⋊ C2
derived, SylowC5 ⋊ C2×C9×C11×C19
HallC5×C11×C19 ⋊ C2×C9
HallC5×C9×C19 ⋊ C2×C11
HallC5×C9×C11 ⋊ C2×C19
HallC5×C19 ⋊ C2×C9×C11
HallC5×C11 ⋊ C2×C9×C19
HallC5×C9 ⋊ C2×C11×C19

Subgroups

subgroupG/H
center, hypercenterC9×C11×C19D5
commutator, hypocenterC5C2×C9×C11×C19
FrattiniC3C3×D5×C11×C19
FittingC5×C9×C11×C19C2
socleC3×C5×C11×C19C2×C3
prime radicalC3×D5×C11×C19C3
cosocleC3×C5C2×C3×C11×C19
LCSG ▷ C5
UCSC1 ◁ C9×C11×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9405

Conjugacy classes & character table

7524 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×C11×C19×AGL(1,𝔽5), C9×C11×C19⋊AGL(1,𝔽5), C9×C19×C11⋊AGL(1,𝔽5), …
maximal normal subgroup ofC9×C11×C19×AGL(1,𝔽5), C9×C11×C19⋊AGL(1,𝔽5), C9×C19×C11⋊AGL(1,𝔽5), …
maximal quotient ofC9×C11×C19×Dic5, C2×C9×D5×C11×C19

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 8);