Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
294 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 45 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:
2^6,3,2^2|a^2=d,c^2=f,d^2=e,e^2=f,b^a=bc,g^a=g^2,h^a=hi,c^b=cf,d^b=df,h^g=i,i^g=hi76 conjugacy classes — view the full character table.
| maximal subgroup of | #72342873, #72343063, S4×#350 |
| maximal normal subgroup of | #72342873, #72343063, S4×#350 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1085877);