Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C4 |
| direct product | C2×#83396 |
| Fitting | C2×C3×#535 ⋊ C2 |
| Sylow | C3 ⋊ C2×#3027 |
5110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10949268, #72254310, #72254316, … |
| maximal normal subgroup of | C2×#10949268, #72254310, #72254316, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1036301);