Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Sylow | C3 ⋊ #21795 |
1538 conjugacy classes of subgroups; only the 315 normal subgroups are shown.
This group has 1538 conjugacy classes of subgroups — too many to draw. Only its 315 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=g,b^2=e,b^a=be,c^a=cf,d^a=de,f^a=fh,i^a=i^2,c^b=ce,d^b=dh,g^c=gh90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 178832);