Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C8 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×#4535 |
| Sylow | C33 ⋊ Q8⋊C8 |
700 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
432 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 11900);