Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of Dic50 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×C22⋊D25 |
| Fitting | C23×C3×C25 ⋊ C2 |
| Hall | C3×C25 ⋊ C2×D4 |
| Sylow | C25 ⋊ C2×C3×D4 |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
318 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 158);