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(C13⋊C3)⋊(D41⋊C5) #30630548

order15990
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C13⋊C3)⋊(D41⋊C5)
unambiguous semidirect product(C41⋊C5)⋊(D13⋊C3)
unambiguous semidirect product((C13⋊C3)⋊D41)⋊C5
unambiguous semidirect product(C13⋊(D41⋊C5))⋊C3

Splittings

Fitting, socle, derived, HallC13×C41 ⋊ C2×C3×C5
HallC13⋊C3×C41⋊C5 ⋊ C2
HallC13⋊(D41⋊C5) ⋊ C3
Hall(C13⋊C3)⋊D41 ⋊ C5
HallC13×C41⋊C5 ⋊ C2×C3
HallC13⋊C3×C41 ⋊ C2×C5
HallD533 ⋊ C3×C5
HallC41⋊C5 ⋊ D13⋊C3
SylowC41 ⋊ C5×D13⋊C3
HallC13⋊C3 ⋊ D41⋊C5
SylowC13 ⋊ C3×D41⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC13×C41C2×C3×C5
LCSG ▷ C13×C41
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 533

Polycyclic presentation:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(#14523821⋊C3)⋊C5, (#14523822⋊C3)⋊C5, D13⋊C3×D41⋊C5, …
maximal normal subgroup of(#14523821⋊C3)⋊C5, (#14523822⋊C3)⋊C5, D13⋊C3×D41⋊C5, …
maximal quotient of(Dic533⋊C3)⋊C5, C2×(C13⋊C3)⋊(D41⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15990, 36);