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(C5⋊(D13⋊C3))⋊D41 #44544374

order31980
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product(C5⋊(D13⋊C3))⋊D41
unambiguous semidirect productD205⋊(D13⋊C3)
unambiguous semidirect product((C13⋊C3)⋊D41)⋊D5
unambiguous semidirect product(D65⋊D41)⋊C3

Splittings

Fitting, socle, derived, HallC5×C13×C41 ⋊ C22×C3
HallD65⋊D41 ⋊ C3
HallC5×C13⋊C3×C41 ⋊ C22
HallC13⋊C3×C41 ⋊ C2×D5
HallC13×C41 ⋊ C2×C3×D5
HallC5×C41 ⋊ C2×D13⋊C3
HallC5×C13⋊C3 ⋊ C2×D41
HallC5×C13 ⋊ C2×C3×D41
SylowC41 ⋊ D5×D13⋊C3
HallC13⋊C3 ⋊ D5×D41
SylowC13 ⋊ C3×D5×D41
SylowC5 ⋊ D13⋊C3×D41

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C13×C41C22×C3
LCSG ▷ C5×C13×C41
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2665

Polycyclic presentation:

2^2,3,5,13,41|e^a=e^12,f^a=f^40,d^b=d^4,e^b=e^12,e^c=e^3

Conjugacy classes & character table

472 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 102);