Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C22×#4711 |
| Fitting | C22×C3×#97 ⋊ C2 |
| Sylow | C3 ⋊ C22×#442 |
3654 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D3×#442, #72219833, #72219845, … |
| maximal normal subgroup of | C22×D3×#442, #72219833, #72219845, … |
| maximal quotient of | #72258593 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1033614);