Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C2×#82936 |
| Fitting | C2×C3×#525 ⋊ C2 |
| Sylow | C3 ⋊ C2×#3025 |
5086 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10826602, #72248117, C2×#10826595, … |
| maximal normal subgroup of | C2×#10826602, #72248117, C2×#10826595, … |
| maximal quotient of | #72255207, #72255223, #72271135, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1036289);