Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #6290 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C3×C4 |
| direct product | C4×(C2×D3)⋊(C3⋊Dic3) |
| Sylow | C33 ⋊ C4×C22⋊C4 |
1980 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 26549);