Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | D3×#2180 |
| Fitting | C3×#2180 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2180 |
646 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
69 conjugacy classes — view the full character table.
| maximal subgroup of | #72222782, #72222804, #72222854, … |
| maximal normal subgroup of | D3×#33468, D3×#33469, D3×#33691, … |
| maximal quotient of | #72222782, #72222804, #72222854, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322997);