Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C3×#342 ⋊ C2 |
| Sylow | C3 ⋊ #23444 |
2418 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|b^a=be,c^a=cf,g^a=gh,i^a=i^2,c^b=cg,d^b=dh,i^b=i^2,e^c=eh,i^c=i^290 conjugacy classes — view the full character table.
| maximal subgroup of | #72248124, D3×#23444, #72248407, … |
| maximal normal subgroup of | #72248124, D3×#23444, #72248407, … |
| maximal quotient of | #72248728, #72253768 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 196821);