Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C3 ⋊ #11157 |
922 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=g,c^2=d,d^2=h,e^2=h,b^a=bd,c^a=ce,d^a=dh,f^a=fh,c^b=cf,d^b=dh,e^b=eh,f^c=fh,g^c=gh,i^c=i^290 conjugacy classes — view the full character table.
| maximal subgroup of | #72248310, #72248329, #72248364, … |
| maximal normal subgroup of | #72248310, #72248329, #72248364, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 77191);