Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×B(4,𝔽2)⋊C3 |
| unambiguous semidirect product | (C4×B(4,𝔽2))⋊C3 |
| Fitting, Sylow | C4×B(4,𝔽2) ⋊ C3 |
| derived | H(5,𝔽2) ⋊ C2×C3×C4 |
440 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 32 |
64 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1083856);