Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#66995 |
| Fitting | C22×Q8×C11 ⋊ C2 |
| Sylow | C11 ⋊ C2×#137 |
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
122 conjugacy classes — view the full character table.
| maximal subgroup of | #13068982, #13068988, #13069086, … |
| maximal normal subgroup of | #13068982, #13068988, #13069086, … |
| maximal quotient of | C2×#10622838, C2×#10622579, C2×#10622577, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 1258);