Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
| direct product | C2×#72141 |
| Sylow | C3 ⋊ C2×#1795 |
3946 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | #72247999, #72248002, #72248003, … |
| maximal normal subgroup of | #72247999, #72248002, #72248003, … |
| maximal quotient of | #72249249, #72271525 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 168903);