Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C11×M16 ⋊ C2 |
| Sylow | C11 ⋊ #421 |
154 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 59 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|c^2=d,d^2=f,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 | #13068578, #13068579, #13068583, … |
| maximal normal subgroup of | #13068578, #13068579, #13068583, … |
| maximal quotient of | #13067001, #13067006, #13067010, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 671);