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C3⋊(C43⋊#63122) #46776564

order33540
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C43⋊#63122)
unambiguous semidirect productC43⋊(C3⋊#63122)

Splittings

Fitting, socle, derived, HallC3×C5×C13×C43 ⋊ C4
HallC5×C13×C43 ⋊ Dic3
HallC3×C13×C43 ⋊ AGL(1,𝔽5)
HallC3×C5×C43 ⋊ #261
HallC13×C43 ⋊ ΓL(1,𝔽16)
HallC5×C43 ⋊ C3⋊#261
HallC3×C5×C13 ⋊ Dic43
HallC3×C43 ⋊ #63122
HallC5×C13 ⋊ Dic129
SylowC43 ⋊ C3⋊#63122
HallC3×C13 ⋊ C43⋊AGL(1,𝔽5)
HallC3×C5 ⋊ C43⋊#261
SylowC13 ⋊ C3⋊(C43⋊AGL(1,𝔽5))
SylowC5 ⋊ C3⋊(C43⋊#261)
SylowC3 ⋊ C43⋊#63122

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C13×C43C4
prime radical, cosocleC3×C43×D65C2
LCSG ▷ C3×C5×C13×C43
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8385

Polycyclic presentation:

2^2,3,5,13,43|a^2=b,c^a=c^2,d^a=d^2,e^a=e^5,f^a=f^42,d^b=d^4,e^b=e^12

Conjugacy classes & character table

2196 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 184);