Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C11 ⋊ #405 |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|a^2=d,c^2=e,d^2=f,e^2=f,g^a=g^10,c^b=cf140 conjugacy classes — view the full character table.
| maximal subgroup of | #13068370, #13068372, #13068415, … |
| maximal normal subgroup of | #13068370, #13068372, #13068415, … |
| maximal quotient of | M16×C11⋊C8, #13066900, #13066903, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 654);