Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C3×#2309 ⋊ C2 |
| Sylow | C3 ⋊ #20945 |
1862 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=g,b^2=egh,d^2=h,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=dh,f^a=fh,i^a=i^2,e^b=eh,g^b=gh,i^b=i^2,f^c=fh,i^c=i^2102 conjugacy classes — view the full character table.
| maximal subgroup of | #72248566, #72248570, #72248581, … |
| maximal normal subgroup of | #72248566, #72248570, #72248581, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 171103);