Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×D4×C25 ⋊ C2 |
| Hall | C3×C25 ⋊ D8 |
| Sylow | C25 ⋊ #213 |
| Sylow | C3 ⋊ #87722 |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 600 |
Polycyclic presentation:
2^4,3,5^2|c^2=d,f^5=g,b^a=bc,c^a=cd,e^a=e^2,f^a=f^4g^4,g^a=g^4,c^b=cd192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 77);