Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C3 ⋊ #12574 |
994 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=e,b^2=f,b^a=bd,d^a=dg,g^a=gh,c^b=ch,e^b=eg,i^b=i^2,e^d=eh90 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#12574, #72248175, #72248197, … |
| maximal normal subgroup of | D3×#12574, #72248175, #72248197, … |
| maximal quotient of | #72249307 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 84514);