Finite Group DatabasebetaFinite Group Databasebeta| order | 4000 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | AGL(1,𝔽5)×D5⋊AGL(1,𝔽5) |
| Fitting, socle, derived, Sylow | C53 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C53 | C2×C42 |
| prime radical | D53 | C22 |
| cosocle | D5×C5⋊D5 | C23 |
| LCS | G ▷ C53 | |
| UCS | C1 | |
536 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
70 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.