Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C210 |
| direct product | C2×#72131 |
| Sylow | C3 ⋊ C2×#1438 |
8190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#1438, C2×#10742700, C2×#10687759, … |
| maximal normal subgroup of | C2×D3×#1438, C2×#10742700, C2×#10687759, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 91226);