Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D3)⋊Dic25 |
| Hall | C3×C25 ⋊ C22⋊C4 |
| Sylow | C25 ⋊ (C2×D3)⋊C4 |
| Sylow | C3 ⋊ C22⋊Dic25 |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
Polycyclic presentation:
2^4,3,5^2|a^2=d,f^5=g,b^a=bc,f^a=f^4g^4,g^a=g^4,e^b=e^2162 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 31);