Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of Dic54 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#88399 |
| Fitting | C2×C42×C27 ⋊ C2 |
| Sylow | C27 ⋊ C4×#41 |
620 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, 2275);