Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#1749 ⋊ C2 |
| Sylow | C3 ⋊ #21379 |
1426 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=g,b^2=eg,d^2=f,g^2=h,b^a=be,c^a=cf,d^a=dh,d^b=dh,i^c=i^2132 conjugacy classes — view the full character table.
| maximal subgroup of | #72269938, #72269976, D3×#21379 |
| maximal normal subgroup of | #72269938, #72269976, D3×#21379 |
| maximal quotient of | #72270348, #72270397 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 174563);