Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C23 |
| direct product | C2×C9⋊(C22⋊SL(2,𝔽3)) |
| unambiguous semidirect product | (C2×C9)⋊(C22⋊SL(2,𝔽3)) |
| Fitting | C23×Q8×C9 ⋊ C3 |
| Sylow | C23×Q8 ⋊ 3−1+2 |
565 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 565 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30932);