Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of 3−1+2⋊Q8 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C210 |
| direct product | C23×#611⋊C3 |
| Fitting | C25×3−1+2 ⋊ C2 |
| Sylow | 3−1+2 ⋊ C23×D4 |
4460 conjugacy classes of subgroups; only the 1204 normal subgroups are shown.
This group has 4460 conjugacy classes of subgroups — too many to draw. Only its 1204 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
248 conjugacy classes — view the full character table.
| maximal subgroup of | C23×D4×AGL(1,ℤ/9), #72268858 |
| maximal normal subgroup of | C23×D4×AGL(1,ℤ/9), #72268858 |
| maximal quotient of | #72268904, #72268918, #72268950 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 31033);