Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C2×C3×C4 |
| direct product | C32×#4693 |
| Fitting | C33×C4×C8 ⋊ C2 |
| Sylow | C33 ⋊ #492 |
1028 conjugacy classes of subgroups; only the 330 normal subgroups are shown.
This group has 1028 conjugacy classes of subgroups — too many to draw. Only its 330 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
486 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 28192);