Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×Q8×((C3⋊D3)⋊C3)⋊C2 |
| Fitting | C2×Q8×H(3,𝔽3) ⋊ C22 |
| Sylow | H(3,𝔽3) ⋊ C23×Q8 |
3131 conjugacy classes of subgroups; only the 619 normal subgroups are shown.
This group has 3131 conjugacy classes of subgroups — too many to draw. Only its 619 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
110 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30829);