Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D3×#2213 |
| Fitting | C3×#2213 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2213 |
790 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
69 conjugacy classes — view the full character table.
| maximal subgroup of | #72214721, D3×#12310, D3×#12314, … |
| maximal normal subgroup of | D3×#12310, D3×#12314, D3×#33688, … |
| maximal quotient of | #72214721, C2×D3×#2213, D3×#13261 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323944);