Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23 |
| direct product | C2×#11722576 |
| Sylow | C2×H(5,𝔽2) ⋊ 3−1+2 |
1108 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 1108 conjugacy classes of subgroups — too many to draw. Only its 169 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
182 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72219862, C2×#10589531⋊C3, C2×C3×#11722576, … |
| maximal normal subgroup of | C2×#72219862, C2×#10589531⋊C3, C2×C3×#11722576, … |
| maximal quotient of | C2×C3×#11722576 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30921);