Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of C3⋊(#127⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3×C4 |
| direct product | C3×C3⋊(#384⋊C3) |
| unambiguous semidirect product | C3⋊(C3×#384⋊C3) |
| unambiguous semidirect product | #4935⋊C32 |
| unambiguous semidirect product | (C3×#4935)⋊C3 |
| derived | C3×C42 ⋊ C32×C4 |
284 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 23093);