Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
| direct product | Dic6×H(5,𝔽2) |
| Sylow | C3 ⋊ Q8×H(5,𝔽2) |
7406 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
153 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1081678);