Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#66972 |
| Fitting | C2×C11×Q16 ⋊ C2 |
| Sylow | C11 ⋊ C2×#135 |
266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | #13070322, #13070327, #13070364, … |
| maximal normal subgroup of | #13070322, #13070327, #13070364, … |
| maximal quotient of | C2×#10622417, C2×#10622493, C2×#10622485, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 1215);