Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×#11722396 |
1518 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 1518 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72220146, C2×#72220152, C22×#11722396 |
| maximal normal subgroup of | C2×#72220152, C22×#11722396 |
| maximal quotient of | C22×#11722396, C2×#13147076 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30572);