Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×Dic6 |
| unambiguous semidirect product | C3⋊(C52×Q8) |
| Hall | C3×C52 ⋊ Q8 |
| Sylow | C3 ⋊ C52×Q8 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
225 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#6655, C5×#6660, C5×#6661, … |
| maximal normal subgroup of | C5×#6655, C5×#6660, C5×#6661, … |
| maximal quotient of | C52×Dic3⋊C4, C52×C4⋊Dic3, C2×C52×Dic6, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 126);