Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #1201 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#6651 |
| Hall | C3×C52 ⋊ M16 |
| Sylow | C52 ⋊ ΓL(1,𝔽25) |
| Sylow | C3 ⋊ C5×#676 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 289);