Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | #60070⋊C3 |
| Fitting, Sylow | #60070 ⋊ C3 |
1057 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 1057 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 64 |
| transitive degree | μt(G) = 64 |
Polycyclic presentation:
3,2^8|b^2=h,f^2=i,b^a=befg,c^a=cdegh,d^a=defg,e^a=dghi,c^b=cg,g^b=gi,h^c=hi,e^d=ei86 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084586);