Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C24×D4 ⋊ D3 |
1528 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 1528 conjugacy classes of subgroups — too many to draw. Only its 71 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|d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^2,h^a=hi,d^c=df,h^g=i,i^g=hi58 conjugacy classes — view the full character table.
| maximal subgroup of | #72227580, #72228089, #72228284, … |
| maximal normal subgroup of | #72228284, #72258796, D8×GL(2,ℤ/4), … |
| maximal quotient of | #72267949, #72271321, #72271435, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1088315);