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C19×C9⋊(C11⋊AGL(1,𝔽5)) #49178388

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

Aliases

direct productC19×C9⋊(C11⋊AGL(1,𝔽5))
unambiguous semidirect productC9⋊(C19×C11⋊AGL(1,𝔽5))
unambiguous semidirect productC11⋊(C19×C9⋊AGL(1,𝔽5))

Splittings

Fitting, HallC5×C9×C11×C19 ⋊ C4
derived, HallC5×C9×C11 ⋊ C4×C19
HallC9×C11×C19 ⋊ AGL(1,𝔽5)
HallC5×C11×C19 ⋊ Dic9
HallC5×C9×C19 ⋊ Dic11
HallC11×C19 ⋊ C9⋊AGL(1,𝔽5)
HallC9×C19 ⋊ C11⋊AGL(1,𝔽5)
HallC9×C11 ⋊ C19×AGL(1,𝔽5)
HallC5×C19 ⋊ Dic99
HallC5×C11 ⋊ C19×Dic9
HallC5×C9 ⋊ C19×Dic11
SylowC11 ⋊ C19×C9⋊AGL(1,𝔽5)
SylowC9 ⋊ C19×C11⋊AGL(1,𝔽5)
SylowC5 ⋊ C19×Dic99

Subgroups

subgroupG/H
center, hypercenterC19C9⋊(C11⋊AGL(1,𝔽5))
commutator, hypocenterC5×C9×C11C4×C19
FrattiniC3C19×C3⋊(C11⋊AGL(1,𝔽5))
FittingC5×C9×C11×C19C4
socleC3×C5×C11×C19Dic3
prime radicalC3×D5×C11×C19D3
cosocleC9×D5×C11C2×C19
LCSG ▷ C5×C9×C11
UCSC1 ◁ C19

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9405

Conjugacy classes & character table

3819 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 97);