Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C2×C3×H(3,ℤ/4) ⋊ C2 |
| Sylow | C3 ⋊ #10742 |
1226 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=g,d^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,g^a=gh,i^a=i^2,e^b=eh,d^c=dh,i^c=i^2102 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#10742, #72248194, #72248215 |
| maximal normal subgroup of | D3×#10742, #72248194, #72248215 |
| maximal quotient of | #72271390 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 74897);