Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C2×#87298 |
| Fitting | C2×C3×#585 ⋊ C2 |
| Sylow | C3 ⋊ C2×#3585 |
11138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10826596, #72248041, #72248049, … |
| maximal normal subgroup of | C2×#10826596, #72248041, #72248049, … |
| maximal quotient of | #72249271, #72253857, #72271719, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1083408);