Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C11×C4⋊C8 ⋊ C2 |
| Sylow | C11 ⋊ #424 |
114 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 55 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|b^2=e,c^2=d,d^2=f,b^a=bf,g^a=g^10,c^b=ce128 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#424, C2×#10622452, #13077177, … |
| maximal normal subgroup of | D11×#424, C2×#10622452, #13077177, … |
| maximal quotient of | #13067385, #13067389, #13067393, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 371);