Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #3746⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C4×#3745⋊C3 |
| unambiguous semidirect product | (C4×#3745)⋊C3 |
| Fitting | C4×C8×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C4×D8 |
513 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 513 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
212 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 7521);