Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #3746⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C4×#3746⋊C3 |
| unambiguous semidirect product | (C4×#3746)⋊C3 |
| Sylow | H(3,𝔽3) ⋊ C4×Q16 |
429 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 429 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) = 576 |
212 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 7511);