Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#66982 |
| Fitting | C23×C4×C11 ⋊ C2 |
| Sylow | C11 ⋊ C2×#123 |
342 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
188 conjugacy classes — view the full character table.
| maximal subgroup of | #13066962, #13066965, #13069026, … |
| maximal normal subgroup of | #13066962, #13066965, #13069026, … |
| maximal quotient of | C2×#10622824, C2×#10622823, C2×#10622826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 1239);