Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| isoclinism | isoclinic class of #4323 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#66901 |
| Sylow | C11 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#66901, #104×Dic11, #13068426, … |
| maximal normal subgroup of | C4×#66901, #104×Dic11, #13068426, … |
| maximal quotient of | C2×D4⋊(C11⋊C8), C2×Q8⋊(C11⋊C8), #13066998, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 767);