Finite Group DatabasebetaFinite Group Databasebeta| order | 8032 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C22⋊D251)⋊C4 |
| Fitting | C22⋊C4×C251 ⋊ C2 |
| Sylow | C251 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D251 |
| commutator | C2×C251 | C22×C4 |
| Fitting | C22⋊C4×C251 | C2 |
| socle | C22×C251 | C23 |
| hypercenter | C22⋊C4 | D251 |
| hypocenter | C251 | C4×D4 |
| LCS | G ▷ C2×C251 ▷ C251 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,251|a^2=e,c^2=e,b^a=bd,f^c=f^2501270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D4×D251, C2×(C22⋊D251)⋊C4, C4×#16860809, … |
| maximal normal subgroup of | C4×D4×D251, C2×(C22⋊D251)⋊C4, C4×#16860809, … |
| maximal quotient of | #30631534, C22⋊C4×Dic251, #30631538, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8032, 106);