Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| isoclinism | isoclinic class of #4323 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#4325 |
| Fitting | C4×Q8×C11 ⋊ C2 |
| Sylow | C11 ⋊ C4×SD16 |
122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 122 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 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #13067413, C8×#4325, #13067426, … |
| maximal normal subgroup of | #13067413, C8×#4325, #13067426, … |
| maximal quotient of | C8×#4325, #13067450, #13067459, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 557);