Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#1057 |
| Sylow | C13 ⋊ Q8⋊C8 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^6,13|a^2=c,b^2=f,c^2=e,d^2=f,b^a=bd,d^a=df,g^a=g^8,d^b=df,g^c=g^1258 conjugacy classes — view the full character table.
| maximal subgroup of | C2×Q8⋊#1057, D13⋊(Q8⋊C8), #13130127, … |
| maximal normal subgroup of | C2×Q8⋊#1057, D13⋊(Q8⋊C8), #13130127, … |
| maximal quotient of | #13129654, #13129656, #13129672, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 268);