Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#67641 |
| Sylow | C3 ⋊ C2×#1393 |
1154 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #72270411, C2×D3×#1393, #72271723 |
| maximal normal subgroup of | #72270411, C2×D3×#1393, #72271723 |
| maximal quotient of | C2×#10682466 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 84535);