Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×#5931 |
| Fitting | C22×C4×Q8 ⋊ D3 |
| derived | C22⋊SL(2,𝔽3) ⋊ C2×C4 |
580 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1090052);