Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C4 |
| direct product | C2×#84126 |
| Fitting | C2×C3×#585 ⋊ C2 |
| Sylow | C3 ⋊ C2×#3027 |
5110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | #72248002, C2×#10949267, #72248013, … |
| maximal normal subgroup of | #72248002, C2×#10949267, #72248013, … |
| maximal quotient of | #72271232, #72271241, #72271550 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1036302);