Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C3×#532 ⋊ C2 |
| Sylow | C3 ⋊ #23573 |
1508 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|d^2=e,f^2=h,b^a=be,c^a=cf,f^a=fh,c^b=cg,d^c=dh,f^c=fh,i^c=i^2108 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#23573, #72269976, #72270038 |
| maximal normal subgroup of | D3×#23573, #72269976, #72270038 |
| maximal quotient of | #72271630 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 197787);