Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊C4×SL(2,𝔽3) |
| unambiguous semidirect product | (C2×Q8×C22⋊C4)⋊C3 |
| Fitting, Sylow | C2×Q8×C22⋊C4 ⋊ C3 |
1574 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 1574 conjugacy classes of subgroups — too many to draw. Only its 245 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 128 |
140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084164);