Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×C22⋊C8 ⋊ D3 |
825 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 825 conjugacy classes of subgroups — too many to draw. Only its 63 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=f,c^2=e,e^2=f,c^a=ce,e^a=ef,g^a=g^2,h^a=hi,c^b=cd,h^g=i,i^g=hi58 conjugacy classes — view the full character table.
| maximal subgroup of | #72225957, #72226209, #72226284, … |
| maximal normal subgroup of | #72226209, #72226284, #72226310 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1087725);