Finite Group DatabasebetaFinite Group Databasebeta| order | 8032 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C251⋊#95 |
| Sylow | C251 ⋊ #95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×D251 |
| commutator | C2×C251 | C42 |
| Fitting | C22×C4×C251 | C2 |
| socle | C23×C251 | C22 |
| hypercenter | C22×C4 | D251 |
| hypocenter | C251 | #95 |
| LCS | G ▷ C2×C251 ▷ C251 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,251|a^2=d,b^2=e,b^a=bc,f^b=f^2502020 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30631421, #30631422, #30631424, … |
| maximal normal subgroup of | #30631421, #30631422, #30631424, … |
| maximal quotient of | #30631441, #30631442, #30631443, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8032, 53);