Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C213 |
| direct product | C22×#4955 |
| Fitting | C23×C3×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ C22×#379 |
33214 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#76753, C22×#74884, C22×#82604, … |
| maximal normal subgroup of | C22×#76753, C22×#74884, C22×#82604, … |
| maximal quotient of | #72271192, #72271283 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 327822);