Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C23×SD16 ⋊ D3 |
758 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 61 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=e,c^2=f,d^2=f,b^a=be,c^a=ce,g^a=g^2,h^a=hi,c^b=cd,d^b=df,d^c=df,h^g=i,i^g=hi58 conjugacy classes — view the full character table.
| maximal subgroup of | #72226209, SD16×GL(2,ℤ/4), #72228332, … |
| maximal normal subgroup of | #72226209, SD16×GL(2,ℤ/4), #72228332, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1088025);