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C11⋊(C19⋊#4380) #49178652

order37620
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect productC11⋊(C19⋊#4380)
unambiguous semidirect productC19⋊(C11⋊#4380)

Splittings

Fitting, socle, derived, HallC32×C5×C11×C19 ⋊ C4
HallC32×C11×C19 ⋊ AGL(1,𝔽5)
HallC5×C11×C19 ⋊ #157
HallC32×C5×C19 ⋊ Dic11
HallC32×C5×C11 ⋊ Dic19
HallC11×C19 ⋊ #4380
HallC32×C19 ⋊ C11⋊AGL(1,𝔽5)
HallC32×C11 ⋊ C19⋊AGL(1,𝔽5)
HallC5×C19 ⋊ C11⋊#157
HallC5×C11 ⋊ C19⋊#157
HallC32×C5 ⋊ Dic209
SylowC19 ⋊ C11⋊#4380
SylowC11 ⋊ C19⋊#4380
SylowC32 ⋊ C11⋊(C19⋊AGL(1,𝔽5))
SylowC5 ⋊ C11⋊(C19⋊#157)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C5×C11×C19C4
prime radical, cosocleC11×C19×C3⋊D15C2
LCSG ▷ C32×C5×C11×C19
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6270

Polycyclic presentation:

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

Conjugacy classes & character table

2511 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 361);