Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×#1094⋊Q8 |
| unambiguous semidirect product | (C2×#1094)⋊Q8 |
| unambiguous semidirect product | (C2×(C22⋊C9)⋊Q8)⋊C3 |
634 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30450);