Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of C3⋊(C3⋊S4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22×C33 |
| direct product | C2×C3⋊(C3⋊(A4⋊C8)) |
| unambiguous semidirect product | (C2×C3)⋊(C3⋊(A4⋊C8)) |
| unambiguous semidirect product | (C2×A4)⋊(C3⋊(C3⋊C8)) |
| derived | C32×A4 ⋊ C2×C8 |
886 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 886 conjugacy classes of subgroups — too many to draw. Only its 275 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 39121);