Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#70019 |
| Fitting | C22×C3×#99 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2127 |
1510 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#2127, #72248312, #72248315, … |
| maximal normal subgroup of | C2×D3×#2127, #72248312, #72248315, … |
| maximal quotient of | #72253523 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322351);