Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #88521 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | C22×#88521 |
| Sylow | C3×C9 ⋊ C22×Q16 |
1290 conjugacy classes of subgroups; only the 431 normal subgroups are shown.
This group has 1290 conjugacy classes of subgroups — too many to draw. Only its 431 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1728 |
444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 20368);