Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Hall | C3×C52 ⋊ Q16 |
| Sylow | C52 ⋊ #216 |
| Sylow | C3 ⋊ #87812 |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1200 |
Polycyclic presentation:
2^4,3,5^2|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,f^a=f^4,g^a=g^4,c^b=cd,e^b=e^2120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 324);