Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | D12×C25 |
| unambiguous semidirect product | C4⋊(D3×C25) |
| Fitting | C3×C4×C25 ⋊ C2 |
| Hall | C3×C25 ⋊ D4 |
| Sylow | C3 ⋊ D4×C25 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
225 conjugacy classes — view the full character table.
| maximal subgroup of | #11924807, #11924808, #11924809, … |
| maximal normal subgroup of | #11924807, #11924808, #11924809, … |
| maximal quotient of | C25×#204, C25×D24, C25×Dic12, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 22);