Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#66997 |
| Sylow | C11 ⋊ C2×C4⋊Q8 |
290 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #13069006, #13069007, #13069009, … |
| maximal normal subgroup of | #13069006, #13069007, #13069009, … |
| maximal quotient of | C2×#10622589, C2×#10622585, C2×#10622587, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 1260);