Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #464 |
112 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 39 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=e,b^2=ef,d^2=f,c^a=cef,g^a=g^10,c^b=cd,d^b=df,d^c=df89 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#464, C2×#10622380, #13078064, … |
| maximal normal subgroup of | D11×#464, C2×#10622380, #13078064, … |
| maximal quotient of | #13068031, #13068045, #13068059, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 299);