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C9×C11×C19⋊AGL(1,𝔽5) #49178371

order37620
automorphism?
homologyAbelianization (H1) = C4×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC9×C11×C19⋊AGL(1,𝔽5)

Splittings

Fitting, HallC5×C9×C11×C19 ⋊ C4
derived, HallC5×C19 ⋊ C4×C9×C11
HallC9×C11×C19 ⋊ AGL(1,𝔽5)
HallC5×C11×C19 ⋊ C4×C9
HallC5×C9×C19 ⋊ C4×C11
HallC5×C9×C11 ⋊ Dic19
HallC11×C19 ⋊ C9×AGL(1,𝔽5)
HallC9×C19 ⋊ C11×AGL(1,𝔽5)
HallC5×C11 ⋊ C9×Dic19
HallC5×C9 ⋊ C11×Dic19
SylowC19 ⋊ C9×C11×AGL(1,𝔽5)
SylowC5 ⋊ C9×C11×Dic19

Subgroups

subgroupG/H
center, hypercenterC9×C11C19⋊AGL(1,𝔽5)
commutator, hypocenterC5×C19C4×C9×C11
FrattiniC3C3×C11×C19⋊AGL(1,𝔽5)
FittingC5×C9×C11×C19C4
socleC3×C5×C11×C19C3×C4
prime radicalC3×D5×C11×C19C2×C3
cosocleC3×D5×C19C2×C3×C11
LCSG ▷ C5×C19
UCSC1 ◁ C9×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9405

Conjugacy classes & character table

4059 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 80);