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C3⋊(#14523823⋊C5) #44544331

order31980
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(#14523823⋊C5)
unambiguous semidirect product(C3⋊#14523823)⋊C5

Splittings

Fitting, socle, derived, HallC3×C13×C41 ⋊ C4×C5
HallC3×C13×C41⋊C5 ⋊ C4
HallC3⋊#14523823 ⋊ C5
HallC13×C41⋊C5 ⋊ Dic3
HallC3×C41⋊C5 ⋊ #261
HallC13×C41 ⋊ C5×Dic3
HallC41⋊C5 ⋊ C3⋊#261
HallC3×C41 ⋊ C5×#261
SylowC41 ⋊ C5×C3⋊#261
HallC3×C13 ⋊ Dic41⋊C5
SylowC13 ⋊ C3⋊(Dic41⋊C5)
SylowC3 ⋊ #14523823⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C13×C41C4×C5
prime radicalC3×D13×C41⋊C5C2
cosocleC3×D13×C41C2×C5
LCSG ▷ C3×C13×C41
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1599

Polycyclic presentation:

2,5,2,3,13,41|a^2=c,d^a=d^2,e^a=e^5,f^a=f^40,f^b=f^10,e^c=e^12

Conjugacy classes & character table

171 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 59);