Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#2148 ⋊ C2 |
| Sylow | C3 ⋊ #33392 |
1154 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=f,e^2=g,f^2=h,g^2=h,b^a=be,e^a=eg,g^a=gh,e^b=egh,f^b=fh,g^b=gh,d^c=dh,i^c=i^2,i^d=i^290 conjugacy classes — view the full character table.
| maximal subgroup of | #72222830, #72222835, #72222851, … |
| maximal normal subgroup of | D3×#33392, #72258527, #72258533, … |
| maximal quotient of | #72222830, #72222835, #72222851 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322532);