Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C2×C3×C5×Dic6 |
| unambiguous semidirect product | (C2×C3)⋊(C3×C5×Q8) |
| Hall | C32×C5 ⋊ C2×Q8 |
| Sylow | C32 ⋊ C2×C5×Q8 |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#90962, C3×#90972, C3×#90973, … |
| maximal normal subgroup of | C3×#90962, C3×#90972, C3×#90973, … |
| maximal quotient of | C3×C4×C5×Dic6, C3×C5×#869, C3×C5×#870, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 719);