Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | #87811⋊C3 |
| Fitting | C52×Q8 ⋊ C2×C3 |
| Hall | #87811 ⋊ C3 |
| Hall | C52⋊C3 ⋊ SD16 |
| Sylow | C52 ⋊ C3×SD16 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^2,3,2^2,5^2|b^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^4,g^a=g^4,d^b=de,f^c=fg,g^c=f^2g^341 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 257);