Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C2×C3×#407 ⋊ C2 |
| Sylow | C3 ⋊ #20598 |
5982 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=g,e^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eh,i^a=i^2,e^b=eh,i^b=i^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #72247861, #72248576, #72248584, … |
| maximal normal subgroup of | #72247861, #72248576, #72248584, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 168772);