Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q8×C11 ⋊ C2 |
| Sylow | C11 ⋊ #533 |
222 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 109 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=e,d^2=f,d^a=de,g^a=g^10,d^b=df128 conjugacy classes — view the full character table.
| maximal subgroup of | #13067017, #13067035, #13067069, … |
| maximal normal subgroup of | #13067017, #13067035, #13067069, … |
| maximal quotient of | #13071020, #13071090, #13071092, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 1028);