Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #6308 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210×C33 |
| direct product | C23×C4⋊(C3⋊(C3⋊D3)) |
| Fitting | C23×C33×C4 ⋊ C2 |
| Sylow | C33 ⋊ C23×D4 |
19068 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47815);