Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C4×#5077 |
| Fitting | C3×C4×#127 ⋊ C2 |
| Sylow | C3 ⋊ C4×#453 |
1578 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×#453, AGL(1,𝔽5)×#5077, C3×C4×#5077 |
| maximal normal subgroup of | C4×D3×#453, C3×C4×#5077 |
| maximal quotient of | AGL(1,𝔽5)×#5077, C3×C4×#5077 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 175440);