Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
| direct product | C2×#70022 |
| Fitting | C22×C3×#99 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1889 |
3566 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #72247581, C2×D3×#1889, #72247737, … |
| maximal normal subgroup of | #72247581, C2×D3×#1889, #72247737, … |
| maximal quotient of | #72248492, #72248813, #72254198, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 171179);