Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#72142 |
| Sylow | C3 ⋊ C2×#1790 |
4402 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | #72247653, C2×D3×#1790, #72247726, … |
| maximal normal subgroup of | #72247653, C2×D3×#1790, #72247726, … |
| maximal quotient of | C2×#10710946, #72248665, C2×#10687758, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 168828);