Finite Group DatabasebetaFinite Group Databasebeta| order | 8032 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊(C251⋊C8) |
| Sylow | C251 ⋊ C22⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×D251 |
| commutator | C2×C251 | C2×C8 |
| Fitting | C22×C4×C251 | C2 |
| socle | C22×C251 | C2×C4 |
| hypercenter | C22×C4 | D251 |
| hypocenter | C251 | C22⋊C8 |
| LCS | G ▷ C2×C251 ▷ C251 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,251|a^2=d,d^2=e,b^a=bc,f^a=f^2502020 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30631410, #30631411, #30631412, … |
| maximal normal subgroup of | #30631410, #30631411, #30631412, … |
| maximal quotient of | #30631411, #30631413, D4⋊(C251⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8032, 59);