Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | C2×#67698 |
| Sylow | C3 ⋊ C2×#1390 |
1202 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#1390, #72248021, #72248033, … |
| maximal normal subgroup of | C2×D3×#1390, #72248021, #72248033, … |
| maximal quotient of | #72249306 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 84508);