Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C11 ⋊ #417 |
162 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|a^2=d,e^2=f,c^a=ce,e^a=ef,g^a=g^10,c^b=cf,e^c=ef122 conjugacy classes — view the full character table.
| maximal subgroup of | #13068570, #13068571, #13068575, … |
| maximal normal subgroup of | #13068570, #13068571, #13068575, … |
| maximal quotient of | #13067003, #13067029, #13067055, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 764);