Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#66888 |
| Sylow | C11 ⋊ C2×#101 |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
122 conjugacy classes — view the full character table.
| maximal subgroup of | #13068411, C4×#66888, #13068538, … |
| maximal normal subgroup of | #13068411, C4×#66888, #13068538, … |
| maximal quotient of | C2×#10622107, #13066939, #13066945, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 668);