Finite Group DatabasebetaFinite Group Databasebeta| order | 10000 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4×C5 |
| direct product | #1043×#1044 |
| Fitting, socle, derived, Sylow | C54 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C54 | C42 |
| prime radical, cosocle | C5⋊D52 | C22 |
| LCS | G ▷ C54 | |
| UCS | C1 | |
968 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 968 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 200 |
100 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.