Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C3×C8×C25 ⋊ C2 |
| Hall | C3×C25 ⋊ M16 |
| Sylow | C25 ⋊ ΓL(1,𝔽25) |
| Sylow | C3 ⋊ #87712 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 600 |
Polycyclic presentation:
2^4,3,5^2|b^2=c,c^2=d,f^5=g,b^a=bd,e^a=e^2,f^a=f^4g^4,g^a=g^4306 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 67);