Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C23 |
| direct product | C22⋊C9×#217 |
| unambiguous semidirect product | (C22×#217)⋊C9 |
786 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊C9×(C22⋊C9)⋊C4, #72245131, #217×#1094 |
| maximal normal subgroup of | #217×#1094 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 13367);