Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
| direct product | C2×#11722398 |
| Fitting | C25×C32 ⋊ D3 |
1360 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72213251, C2×#13164261, C22×#11722398 |
| maximal normal subgroup of | C2×#13164261, C22×#11722398 |
| maximal quotient of | C2×#13147078, C22×#11722398 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30574);