Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×C3×#63974 |
| Sylow | C33 ⋊ C22×C22⋊C4 |
3842 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
288 conjugacy classes. The character table is too large to display.
| maximal quotient of | C2×C3×#10591503 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 41158);