Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
| direct product | C2×#70079 |
| Fitting | C22×C3×#100 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1783 |
5942 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #72248026, #72248033, C2×#10909605, … |
| maximal normal subgroup of | #72248026, #72248033, C2×#10909605, … |
| maximal quotient of | #72248352 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 168715);