Finite Group DatabasebetaFinite Group Databasebeta| order | 784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D49)⋊C4 |
| Fitting | C2×C4×C49 ⋊ C2 |
| Sylow | C49 ⋊ C22⋊C4 |
51 conjugacy classes of subgroups.
| transitive degree | μt(G) = 392 |
Polycyclic presentation:
2^4,7^2|b^2=c,e^7=f,b^a=bd,e^a=e^6f^6,f^a=f^6202 conjugacy classes — view the full character table.
| maximal subgroup of | #13095901, C4×D196, #13095904, … |
| maximal normal subgroup of | #13095901, C4×D196, #13095904, … |
| maximal quotient of | #13095845, #13095846, #13095849, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(784, 13);