Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| isoclinism | isoclinic class of Dic22 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#4339 |
| Fitting | C2×C42×C11 ⋊ C2 |
| Sylow | C11 ⋊ C4×#41 |
310 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 159 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | #13066996, #13066999, #13067001, … |
| maximal normal subgroup of | #13066996, #13066999, #13067001, … |
| maximal quotient of | C4×#66979, C4×#66925, C42×C22⋊D11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 924);