Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C32×#5077 |
| Fitting | C33×#127 ⋊ C2 |
| Sylow | C33 ⋊ #453 |
1440 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 1440 conjugacy classes of subgroups — too many to draw. Only its 234 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 | C3×#10588757⋊C3, 3−1+2×#5077, C3×#11864777, … |
| maximal normal subgroup of | 3−1+2×#5077, C3×#11864777, C3×D3×#5077, … |
| maximal quotient of | C3×#10588757⋊C3, 3−1+2×#5077, C2×C32×#5077 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 28576);