Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C9 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×C9×Dic3⋊C4 |
| Sylow | C3×C9 ⋊ C4×C4⋊C4 |
690 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
648 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 8454);