Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C5 |
| direct product | Q16×C52⋊C3 |
| unambiguous semidirect product | (C52×Q16)⋊C3 |
| Fitting, Hall | C52×Q16 ⋊ C3 |
| Sylow | C52 ⋊ C3×Q16 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
77 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 382);