Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C13 ⋊ #413 |
150 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^6,13|a^2=d,d^2=f,c^a=ce,e^a=ef,g^a=g^8,c^b=cf,d^c=df,g^d=g^1252 conjugacy classes — view the full character table.
| maximal subgroup of | #13129926, #13129935, #13130594, … |
| maximal normal subgroup of | #13129926, #13129935, #13130594, … |
| maximal quotient of | #13130068, #13130070, #13130072, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1114);