Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| isoclinism | isoclinic class of #4323 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#4325 |
| Fitting | C22×Q8×C11 ⋊ C2 |
| Sylow | C11 ⋊ C22×SD16 |
298 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #13068947, #13068953, #13068969, … |
| maximal normal subgroup of | #13068947, #13068953, #13068969, … |
| maximal quotient of | C22×#66873, C22×#66899, C22×#66872, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 1257);