Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #13186 |
310 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=fg,c^2=e,d^2=g,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,g^a=gh,i^a=i^2,d^b=dg,f^b=fh,g^b=gh,i^b=i^2102 conjugacy classes — view the full character table.
| maximal subgroup of | #72226023, #72226101, #72228276, … |
| maximal normal subgroup of | #72226023, #72226101, #72228276, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 87710);