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C11⋊(#4294⋊AGL(1,𝔽5)) #49178346

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

Aliases

unambiguous semidirect productC11⋊(#4294⋊AGL(1,𝔽5))
unambiguous semidirect product#4294⋊(C11⋊AGL(1,𝔽5))

Splittings

derived, HallC5×C11×C19 ⋊ C4×C9
HallC5×C11×#4294 ⋊ C4
HallC11⋊(C19⋊AGL(1,𝔽5)) ⋊ C9
HallC11×#4294 ⋊ AGL(1,𝔽5)
HallC5×#4294 ⋊ Dic11
HallC11×C19 ⋊ C9×AGL(1,𝔽5)
Hall#4294 ⋊ C11⋊AGL(1,𝔽5)
HallC5×C19 ⋊ C9×Dic11
HallC5×C11 ⋊ #4294⋊C4
SylowC19 ⋊ C9×C11⋊AGL(1,𝔽5)
SylowC11 ⋊ #4294⋊AGL(1,𝔽5)
SylowC5 ⋊ C11⋊(#4294⋊C4)

Subgroups

subgroupG/H
center, Frattini, hypercenterC3C11⋊((C19⋊C3)⋊AGL(1,𝔽5))
commutator, hypocenterC5×C11×C19C4×C9
Fitting, socleC3×C5×C11×C19C3×C4
prime radical, cosocleC3×D5×C11×C19C2×C3
LCSG ▷ C5×C11×C19
UCSC1 ◁ C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9405

Polycyclic presentation:

2,3,2,5,11,19,3|a^2=c,b^3=g,d^a=d^2,e^a=e^10,f^a=f^18,f^b=f^7,d^c=d^4

Conjugacy classes & character table

621 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 55);