Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C22×C3×H(5,𝔽2) ⋊ C2 |
| Sylow | C3 ⋊ #32888 |
4070 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|e^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eh,i^a=i^2,e^b=eh,f^b=fh,e^c=eh117 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#32888, #72252279, #72258077, … |
| maximal normal subgroup of | D3×#32888, #72270000, #72270059 |
| maximal quotient of | #72252279, #72252303 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 318266);