Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#67000 |
| Fitting | C22×Q8×C11 ⋊ C2 |
| Sylow | C11 ⋊ C2×#124 |
330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #13069001, #13069017, #13069019, … |
| maximal normal subgroup of | #13069001, #13069017, #13069019, … |
| maximal quotient of | C2×#10622590, C2×#10622603, C2×#10622601, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 1264);