Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
945 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 945 conjugacy classes of subgroups — too many to draw. Only its 73 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:
2^6,3,2^2|a^2=e,b^2=c,b^a=bd,d^a=df,g^a=g^2,h^a=hi,e^b=ef,h^g=i,i^g=hi64 conjugacy classes — view the full character table.
| maximal subgroup of | #72268864, #72268873, #72268915 |
| maximal normal subgroup of | #72268864 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1085675);