Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C24 |
| direct product | C9×#5032 |
| Fitting | C3×C9×#120 ⋊ C2 |
| Sylow | C3×C9 ⋊ B(4,𝔽2) |
724 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×#10588712, #72220121, 3−1+2×#5032, … |
| maximal normal subgroup of | 3−1+2×#5032, #72220167 |
| maximal quotient of | C9×#10588712, #72220121 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 8876);