Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| isoclinism | isoclinic class of #4314 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#66883 |
| Sylow | C11 ⋊ C2×#108 |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
188 conjugacy classes — view the full character table.
| maximal subgroup of | #13066709, #13066710, #13066711, … |
| maximal normal subgroup of | #13066709, #13066710, #13066711, … |
| maximal quotient of | C2×#10622095, C2×#10622096, #13067364, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 639);