Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| isoclinism | isoclinic class of #3358⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×#3359⋊C3 |
| unambiguous semidirect product | (C2×#3359)⋊C3 |
| Fitting, Sylow | C2×#3359 ⋊ C3 |
568 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 128 |
98 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084822);