Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #12575 |
810 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=e,b^2=f,c^2=h,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 | #72253934, #72253938, #72253947, … |
| maximal normal subgroup of | #72253934, #72253938, #72253947, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 84518);