Finite Group DatabasebetaFinite Group Databasebeta| order | 8032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16860810 |
| Fitting | C22×C4×C251 ⋊ C2 |
| Sylow | C251 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D251 |
| commutator | C2×C251 | C24 |
| Frattini | C2 | C23×D251 |
| Fitting | C22×C4×C251 | C2 |
| socle | C22×C251 | C23 |
| hypercenter | C22×C4 | D251 |
| hypocenter | C251 | C2×#41 |
| LCS | G ▷ C2×C251 ▷ C251 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
164 conjugacy classes of subgroups.
2020 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30631652, #30631653, #30631655, … |
| maximal normal subgroup of | #30631652, #30631653, #30631655, … |
| maximal quotient of | C2×#22548672, C2×#22548674, C2×C4×C22⋊D251, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8032, 189);