Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #625 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×C3×(C2×D3)⋊(C3⋊C8) |
| Sylow | C33 ⋊ C2×C22⋊C8 |
1250 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 24157);