Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#1999 ⋊ 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^d=i^284 conjugacy classes — view the full character table.
| maximal subgroup of | #72269876, #72269936, D3×#23573, … |
| maximal normal subgroup of | #72269876, #72269936, D3×#23573, … |
| maximal quotient of | #72270166, #72271409 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 197786);