Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×C22⋊C4×D27 |
| Fitting | C2×C22⋊C4×C27 ⋊ C2 |
| Sylow | C27 ⋊ C22×C22⋊C4 |
1348 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 283 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 2286);