Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#70024 |
| Fitting | C22×C3×#99 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1913 |
2078 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#1913, C2×#10710945, #72248357, … |
| maximal normal subgroup of | C2×D3×#1913, C2×#10710945, #72248357, … |
| maximal quotient of | #72248813, C2×#10693084 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 171577);