Finite Group DatabasebetaFinite Group Databasebeta| order | 36660 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C47⋊(#63118⋊C3) |
| unambiguous semidirect product | (C47⋊#63118)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C13×C47 | C3×C4 |
| prime radical | C5×C47×D13⋊C3 | C2 |
| cosocle | C5×D13×C47 | C2×C3 |
| LCS | G ▷ C5×C13×C47 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3055 |
Polycyclic presentation:
2,3,2,5,13,47|a^2=c,d^a=d^4,e^a=e^5,f^a=f^46,e^b=e^9,e^c=e^12949 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36660, 38);