Finite Group DatabasebetaFinite Group Databasebeta| order | 8032 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q16×D251 |
| Fitting | Q16×C251 ⋊ C2 |
| Sylow | C251 ⋊ C2×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D251 |
| commutator | C4×C251 | C23 |
| Frattini | C4 | C22×D251 |
| Fitting | Q16×C251 | C2 |
| socle | C2×C251 | C2×D4 |
| hypercenter | Q16 | D251 |
| hypocenter | C251 | C2×Q16 |
| LCS | G ▷ C4×C251 ▷ C2×C251 ▷ C251 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q16 | |
60 conjugacy classes of subgroups.
889 conjugacy classes — view the full character table.
| maximal subgroup of | SD32×D251, Q32×D251, #30632126, … |
| maximal normal subgroup of | SD32×D251, Q32×D251, #30632126, … |
| maximal quotient of | #103×D251, #107×D251, #30631779, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8032, 162);