Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52×C8 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C52×#170 |
| derived | C5 ⋊ C2×C52×C8 |
| Sylow | C53 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C52 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C2×C52×C8 |
| Frattini | C2 | C2×C52×AGL(1,𝔽5) |
| Fitting, socle, prime radical | C22×C53 | C4 |
| cosocle | Dic5 | C22×C52 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C22×C52 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
500 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 748);