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(#14523824⋊C3)⋊C5 #44544314

order31980
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(#14523824⋊C3)⋊C5
unambiguous semidirect product(#14523824⋊C5)⋊C3

Splittings

Fitting, socle, derived, HallC13×C41 ⋊ C3×C4×C5
Hall#14523824⋊C5 ⋊ C3
HallC13⋊C3×C41⋊C5 ⋊ C4
Hall#14523824⋊C3 ⋊ C5
HallC13×C41⋊C5 ⋊ C3×C4
Hall#14523824 ⋊ C3×C5
HallC13⋊C3×C41 ⋊ C4×C5
HallC41⋊C5 ⋊ Dic13⋊C3
SylowC41 ⋊ C5×Dic13⋊C3
HallC13⋊C3 ⋊ #4223⋊C5
SylowC13 ⋊ C3×#4223⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC13×C41C3×C4×C5
prime radicalC13⋊C3×D41⋊C5C2
cosocleC13×D41C2×C3×C5
LCSG ▷ C13×C41
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 533

Polycyclic presentation:

2,3,5,2,13,41|a^2=d,e^a=e^12,f^a=f^32,e^b=e^3,f^c=f^10,f^d=f^40

Conjugacy classes & character table

94 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 42);