Finite Group Databasebeta

← Prev (#49178371) Next (#49178373) →

C9×C19×C11⋊AGL(1,𝔽5) #49178372

order37620
automorphism?
homologyAbelianization (H1) = C4×C9×C19 · Schur multiplier (H2) = C1

Aliases

direct productC9×C19×C11⋊AGL(1,𝔽5)
unambiguous semidirect productC11⋊(C9×C19×AGL(1,𝔽5))

Splittings

Fitting, HallC5×C9×C11×C19 ⋊ C4
derived, HallC5×C11 ⋊ C4×C9×C19
HallC9×C11×C19 ⋊ AGL(1,𝔽5)
HallC5×C11×C19 ⋊ C4×C9
HallC5×C9×C19 ⋊ Dic11
HallC5×C9×C11 ⋊ C4×C19
HallC11×C19 ⋊ C9×AGL(1,𝔽5)
HallC9×C11 ⋊ C19×AGL(1,𝔽5)
HallC5×C19 ⋊ C9×Dic11
HallC5×C9 ⋊ C19×Dic11
SylowC11 ⋊ C9×C19×AGL(1,𝔽5)
SylowC5 ⋊ C9×C19×Dic11

Subgroups

subgroupG/H
center, hypercenterC9×C19C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C4×C9×C19
FrattiniC3C3×C19×C11⋊AGL(1,𝔽5)
FittingC5×C9×C11×C19C4
socleC3×C5×C11×C19C3×C4
prime radicalC3×D5×C11×C19C2×C3
cosocleC3×D5×C11C2×C3×C19
LCSG ▷ C5×C11
UCSC1 ◁ C9×C19

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9405

Conjugacy classes & character table

4275 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 81);