Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C11×C4⋊C4 ⋊ C2 |
| Sylow | C11 ⋊ #385 |
234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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=f,c^2=d,b^a=be,g^a=g^10,c^b=cf128 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#385, C2×#10622602, #13071053, … |
| maximal normal subgroup of | D11×#385, C2×#10622602, #13071053, … |
| maximal quotient of | (C2×D11)⋊#95, #13066847, #13066848, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 521);