Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#70729 |
| Fitting | C2×C3×#430 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2091 |
1102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10909609, C2×#10909606, C2×#10909602, … |
| maximal normal subgroup of | C2×#10909609, C2×#10909606, C2×#10909602, … |
| maximal quotient of | #72270040, #72270305 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 199314);