Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C1 |
| direct product | Dic6×C25 |
| unambiguous semidirect product | C3⋊(Q8×C25) |
| Hall | C3×C25 ⋊ Q8 |
| Sylow | C3 ⋊ Q8×C25 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
225 conjugacy classes — view the full character table.
| maximal subgroup of | #11924811, #11924812, #11924813, … |
| maximal normal subgroup of | #11924811, #11924812, #11924813, … |
| maximal quotient of | C25×Dic3⋊C4, C25×C4⋊Dic3, C2×Dic6×C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 20);