Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C3×#3549 ⋊ C2 |
| Sylow | C3 ⋊ #33559 |
1248 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1248 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^8,3|d^2=h,b^a=be,c^a=cf,g^a=gh,i^a=i^2,d^b=dh,f^b=fgh,d^c=dh,e^c=eg,f^e=fh72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#33559, #72255248, #72255253 |
| maximal normal subgroup of | D3×#33559, #72255248, #72255253 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323700);