Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic7⋊C32 |
| Sylow | C7 ⋊ C4⋊C32 |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=d,b^2=c,d^2=e,e^2=f,f^2=g,b^a=bc,h^b=h^6272 conjugacy classes — view the full character table.
| maximal subgroup of | D7×C4⋊C32, C2×Dic7⋊C32, #13274277, … |
| maximal normal subgroup of | D7×C4⋊C32, C2×Dic7⋊C32, #13274277, … |
| maximal quotient of | #13241461, #13241468, #13241482, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 162);