Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
198 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 37 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=d,b^2=c,c^2=e,d^2=f,e^2=f,b^a=bd,g^a=g^2,h^a=hi,d^b=df,h^g=i,i^g=hi76 conjugacy classes — view the full character table.
| maximal subgroup of | S4×#364, #72343063, #72343077 |
| maximal normal subgroup of | S4×#364, #72343063, #72343077 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1085924);