Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#84002 |
| Fitting | C2×C3×#575 ⋊ C2 |
| Sylow | C3 ⋊ C2×#3068 |
2746 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#3068, C2×#10909602, C2×#10909601, … |
| maximal normal subgroup of | C2×D3×#3068, C2×#10909602, C2×#10909601, … |
| maximal quotient of | #72270216, #72270521 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1036974);