Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #625 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C3×C4×(C2×D3)⋊Dic3 |
| Sylow | C33 ⋊ C4×C22⋊C4 |
1538 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, 24257);