Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#66989 |
| 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 | #13069002, #13069004, #13069016, … |
| maximal normal subgroup of | #13069002, #13069004, #13069016, … |
| maximal quotient of | C2×#10622590, C2×#10622558, C2×#10622834, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 1247);