Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C52 · Schur multiplier (H2) = C23×C5 |
| direct product | C22×C52×AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C2×C4×C52) |
| Fitting, socle | C22×C53 ⋊ C4 |
| derived | C5 ⋊ C22×C4×C52 |
| Sylow | C53 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C52 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C22×C4×C52 |
| Frattini | C1 | G |
| Fitting, socle | C22×C53 | C4 |
| prime radical | C22×C52×D5 | C2 |
| cosocle | D5 | C23×C52 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C22×C52 | |
492 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
500 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×AGL(1,𝔽5)×C5⋊D5, C5×AGL(1,𝔽5)×C22⋊D5, C2×C5×Dic5×AGL(1,𝔽5) |
| maximal normal subgroup of | C22×AGL(1,𝔽5)×C5⋊D5, C5×AGL(1,𝔽5)×C22⋊D5, C2×C5×Dic5×AGL(1,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 948);