Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D75⋊Q8 |
| Hall | C3×C25 ⋊ C2×Q8 |
| Sylow | C25 ⋊ D3×Q8 |
| Sylow | C3 ⋊ Q8×D25 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
Polycyclic presentation:
2^4,3,5^2|a^2=d,b^2=d,c^2=d,f^5=g,c^a=cd,f^a=f^4g^4,g^a=g^4,c^b=cd,e^b=e^2123 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 123);