Finite Group DatabasebetaFinite Group Databasebeta| order | 4000 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C5 |
| direct product | C22×D5⋊#1044 |
| Fitting, socle | C22×C53 ⋊ C2×C4 |
| derived, Sylow | C53 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D5⋊#1044 |
| commutator, hypocenter | C53 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C53 | C2×C4 |
| prime radical | C22×D5×C5⋊D5 | C2 |
| cosocle | C5⋊(C5⋊D5) | C24 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C22 | |
1556 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1556 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
136 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.