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C47⋊(#63122⋊C3) #49144010

order36660
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC47⋊(#63122⋊C3)
unambiguous semidirect product(C47⋊#63122)⋊C3

Splittings

Fitting, socle, derived, HallC5×C13×C47 ⋊ C3×C4
HallC47⋊#63122 ⋊ C3
HallC5×C13⋊C3×C47 ⋊ C4
HallC13⋊C3×C47 ⋊ AGL(1,𝔽5)
HallC13×C47 ⋊ C3×AGL(1,𝔽5)
HallC5×C47 ⋊ AGL(1,𝔽13)
HallC5×C13⋊C3 ⋊ Dic47
HallC5×C13 ⋊ C3×Dic47
SylowC47 ⋊ #63122⋊C3
HallC13⋊C3 ⋊ C47⋊AGL(1,𝔽5)
SylowC13 ⋊ C3×C47⋊AGL(1,𝔽5)
SylowC5 ⋊ C47⋊AGL(1,𝔽13)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C13×C47C3×C4
prime radicalC47×C5⋊(D13⋊C3)C2
cosocleC47×D65C2×C3
LCSG ▷ C5×C13×C47
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3055

Polycyclic presentation:

2,3,2,5,13,47|a^2=c,d^a=d^2,e^a=e^5,f^a=f^46,e^b=e^9,d^c=d^4,e^c=e^12

Conjugacy classes & character table

526 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36660, 30);