Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×#208 |
| Hall | C32×C5 ⋊ M16 |
| Sylow | C32 ⋊ C5×M16 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#90958, C3×#90960, C3×#90961, … |
| maximal normal subgroup of | C3×#90958, C3×#90960, C3×#90961, … |
| maximal quotient of | C3×C5×#803, C3×C5×C4⋊(C3⋊C8), C3×C5×#830, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 325);