Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C3×#379 ⋊ C2 |
| Sylow | C3 ⋊ #23984 |
2810 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 2810 conjugacy classes of subgroups — too many to draw. Only its 187 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|b^2=e,b^a=be,c^a=cf,d^a=de,g^a=gh,i^a=i^2,c^b=cg,f^b=fh102 conjugacy classes — view the full character table.
| maximal subgroup of | #72258856, D3×#23984, #72271147, … |
| maximal normal subgroup of | #72258856, D3×#23984, #72271147, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 202015);