Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C4⋊Q8×D27 |
| Fitting | C27×C4⋊Q8 ⋊ C2 |
| Sylow | C27 ⋊ C2×C4⋊Q8 |
580 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 864 |
210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 2525);