Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C23×C22⋊C4 ⋊ D3 |
1635 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 1635 conjugacy classes of subgroups — too many to draw. Only its 101 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=d,b^a=bf,g^a=g^2,h^a=hi,c^b=ce,h^g=i,i^g=hi76 conjugacy classes — view the full character table.
| maximal subgroup of | #72259035, #72259036, C22⋊C4×GL(2,ℤ/4), … |
| maximal normal subgroup of | #72259035, #72259036, C22⋊C4×GL(2,ℤ/4), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1086097);