Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×Dic11 |
| Sylow | C11 ⋊ C2×C4×Q8 |
298 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #101×Dic11, #103×Dic11, #13068448, … |
| maximal normal subgroup of | #101×Dic11, #103×Dic11, #13068448, … |
| maximal quotient of | C2×C4⋊C4×Dic11, C4×Q8×Dic11, C2×#10622594, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 1261);