Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#67001 |
| Sylow | C11 ⋊ C2×#131 |
266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #13068418, #13068419, #13068454, … |
| maximal normal subgroup of | #13068418, #13068419, #13068454, … |
| maximal quotient of | C2×#10622610, C4×#67001, C2×#10622847, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 1268);