Finite Group DatabasebetaFinite Group Databasebeta| order | 15600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | D52×AGL(1,𝔽13) |
| Fitting, socle, derived, Hall | C52×C13 ⋊ C22×C3×C4 |
| Hall | D52×#261 ⋊ C3 |
| Hall | C52×C13⋊C3 ⋊ C22×C4 |
| Hall | C13⋊C3 ⋊ C4×D52 |
| Sylow | C52 ⋊ C22×AGL(1,𝔽13) |
| Sylow | C13 ⋊ C3×C4×D52 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C13 | C22×C3×C4 |
| prime radical | D52×D13⋊C3 | C2 |
| cosocle | C52×D13 | C23×C3 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 | |
496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 130 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽13)×D5⋊AGL(1,𝔽5) |
| maximal normal subgroup of | AGL(1,𝔽13)×D5⋊AGL(1,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.