Finite Group DatabasebetaFinite Group Databasebeta| order | 8032 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×D4×C251 ⋊ C2 |
| Sylow | C251 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,251|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^250,d^b=de1261 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30631853, #30631854, #30631858, … |
| maximal normal subgroup of | #30631853, #30631854, #30631858, … |
| maximal quotient of | #30631686, #30631692, #30631727, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8032, 172);