Finite Group DatabasebetaFinite Group Databasebeta| order | 8032 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C251 ⋊ #103 |
42 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,251|a^2=d,b^2=e,c^2=e,b^a=bc,c^a=ce,f^a=f^250,c^b=ce1264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #103×D251, C2×#22548639, #30631682, … |
| maximal normal subgroup of | #103×D251, C2×#22548639, #30631682, … |
| maximal quotient of | Q8⋊(C251⋊C8), #30631424, #30631433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8032, 70);