Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C11×#99 ⋊ C2 |
| Sylow | C11 ⋊ #410 |
158 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^6,11|a^2=f,c^2=d,g^a=g^10,c^b=ce,d^b=df,e^c=ef77 conjugacy classes — view the full character table.
| maximal subgroup of | #13070254, #13070256, #13070264, … |
| maximal normal subgroup of | #13070254, #13070256, #13070264, … |
| maximal quotient of | #13066927, #13066929, #13066935, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 272);