Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×C3×Q8×C3⋊Dic3 |
| Sylow | C33 ⋊ C2×C4×Q8 |
2412 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 45622);