Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
| direct product | C2×#71654 |
| Fitting | C2×C3×#518 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1889 |
3566 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | #72247574, C2×D3×#1889, #72247726, … |
| maximal normal subgroup of | #72247574, C2×D3×#1889, #72247726, … |
| maximal quotient of | #72248507, #72248725, #72254244, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 171181);