Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C215 |
| direct product | C22×C4×D3×D4 |
| Fitting | C22×C3×C4×D4 ⋊ C2 |
| Sylow | C3 ⋊ C23×C4×D4 |
19998 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D3×#442, D3×#21452, C2×C4×D32×D4, … |
| maximal normal subgroup of | C22×D3×#442, D3×#21452, C22×D3×D42, … |
| maximal quotient of | C22×D3×#442, D3×#60176, C4×D3×#575, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1076129);