Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
| direct product | C4×#4960 |
| Fitting | C2×C3×C4×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ C4×#392 |
3502 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | #72270801, #72270812, #72270909, … |
| maximal normal subgroup of | #72270801, #72270812, #72270909, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 91354);