Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #7099 |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 768 |
Polycyclic presentation:
2^8,3|a^2=d,b^2=c,c^2=e,d^2=f,e^2=g,f^2=h,b^a=bc,c^a=ce,e^a=eg,i^a=i^2,d^b=dg144 conjugacy classes — view the full character table.
| maximal subgroup of | #72244930, D3×#7099, #72244942, … |
| maximal normal subgroup of | #72244930, D3×#7099, #72244942, … |
| maximal quotient of | #72244930, #72245421, #72245494 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 56306);