Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C3⋊(#1039⋊(C37⋊C3)) |
| unambiguous semidirect product | (C3⋊#1039)⋊(C37⋊C3) |
| derived | C3×C52×C37 ⋊ C3×C4 |
| Hall | C3×C52⋊(C37⋊C3) ⋊ C4 |
| Hall | C52×C37 ⋊ C3×Dic3 |
| Sylow | C37 ⋊ C3⋊(#1039⋊C3) |
| Sylow | C52 ⋊ Dic3×C37⋊C3 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6660 |
Polycyclic presentation:
2,3^2,5^2,37,2|a^2=g,c^a=c^2,d^a=d^4,e^a=e^4,d^b=de^3,e^b=d^4e^3,f^b=f^26978 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 386);