Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C3×#3162 ⋊ C2 |
| Sylow | C3 ⋊ #61378 |
1810 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=fh,b^2=f,d^2=f,g^2=h,b^a=bf,c^a=cg,d^a=dh,g^a=gh,i^a=i^2,d^b=df,e^b=eh,i^b=i^2,g^c=gh,i^c=i^284 conjugacy classes — view the full character table.
| maximal subgroup of | #72225908, D3×#61378, #72248862, … |
| maximal normal subgroup of | #72225908, D3×#61378, #72248862, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1050309);