Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C32 |
| direct product | C2×Q8×C22⋊H(3,𝔽3) |
| Fitting | C23×C32×Q8 ⋊ C3 |
| Sylow | C23×Q8 ⋊ H(3,𝔽3) |
1192 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 1192 conjugacy classes of subgroups — too many to draw. Only its 190 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30913);