Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#2196 ⋊ C2 |
| Sylow | C3 ⋊ #33553 |
1252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^8,3|d^2=h,b^a=be,c^a=cf,g^a=gh,d^b=dh,f^b=fgh,e^c=eg,i^d=i^2,f^e=fh54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#33553, C2×#10949263, #72255218, … |
| maximal normal subgroup of | D3×#33553, C2×#10949263, #72255218, … |
| maximal quotient of | #72253970, C2×#10949263, #72269901 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323644);