Finite Group DatabasebetaFinite Group Databasebeta| order | 5200 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | #261×#1043 |
| Fitting, socle, derived, Hall | C52×C13 ⋊ C42 |
| Sylow | C52 ⋊ C4×#261 |
| Sylow | C13 ⋊ C4×#1043 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C13 | C42 |
| prime radical, cosocle | D13×C5⋊D5 | C22 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 325 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | #1043×AGL(1,𝔽13), #261×D5⋊AGL(1,𝔽5) |
| maximal normal subgroup of | #1043×AGL(1,𝔽13), #261×D5⋊AGL(1,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.