Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C3×#342 ⋊ C2 |
| Sylow | C3 ⋊ #25563 |
1608 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|b^2=e,c^2=f,b^a=be,c^a=cf,d^a=de,g^a=gh,i^a=i^2,c^b=cg,f^b=fh,g^c=gh87 conjugacy classes — view the full character table.
| maximal subgroup of | #72271810, #72271812, #72271820, … |
| maximal normal subgroup of | #72271810, #72271812, #72271820, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 222710);