Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C82 · Schur multiplier (H2) = C8 |
| direct product | C5×C8×#170 |
| derived | C5 ⋊ C5×C82 |
| Sylow | C52 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C8 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C5×C82 |
| Frattini | C2×C4 | C2×C5×AGL(1,𝔽5) |
| Fitting | C2×C52×C8 | C4 |
| socle, prime radical | C22×C52 | C42 |
| cosocle | C4×Dic5 | C22×C5 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C5×C8 | |
159 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
400 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2420);