Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
| direct product | C2×#70139 |
| Fitting | C2×C3×#413 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1795 |
3946 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10710735, C2×#10826596, #72248041, … |
| maximal normal subgroup of | C2×#10710735, C2×#10826596, #72248041, … |
| maximal quotient of | #72249240, #72271683 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 168904);