Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C3 ⋊ #12687 |
2508 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 2508 conjugacy classes of subgroups — too many to draw. Only its 147 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:
2^8,3|a^2=f,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^2,f^b=fg,f^d=fh96 conjugacy classes — view the full character table.
| maximal subgroup of | #72219821, D3×#12687, #72230346, … |
| maximal normal subgroup of | #72219821, D3×#12687, #72230346, … |
| maximal quotient of | #72248055, C3×#10710647, C2×#10710647 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 85028);