Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
| direct product | C2×#74919 |
| Fitting | C2×C3×#386 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2684 |
4270 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11427639, C2×#11427637, C2×D3×#2684, … |
| maximal normal subgroup of | C2×#11427639, C2×#11427637, C2×D3×#2684, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 804342);