Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of C3⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | C4×C8×C3⋊D9 |
| Fitting | C3×C4×C8×C9 ⋊ C2 |
| derived, Sylow | C3×C9 ⋊ C2×C4×C8 |
810 conjugacy classes of subgroups; only the 279 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 279 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 864 |
480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 9811);