Finite Group DatabasebetaFinite Group Databasebeta| order | 6240 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×AGL(1,𝔽5)×AGL(1,𝔽13) |
| Fitting, socle | C2×C5×C13 ⋊ C3×C42 |
| derived, Hall | C5×C13 ⋊ C2×C3×C42 |
| Hall | C2×AGL(1,𝔽5)×#261 ⋊ C3 |
| Hall | C5×C13⋊C3 ⋊ C2×C42 |
| Hall | C13⋊C3 ⋊ C2×C4×AGL(1,𝔽5) |
| Sylow | C13 ⋊ C2×C3×C4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×C4×AGL(1,𝔽13) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | AGL(1,𝔽5)×AGL(1,𝔽13) |
| commutator, hypocenter | C5×C13 | C2×C3×C42 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C13 | C3×C42 |
| prime radical | C2×D5×D13⋊C3 | C22 |
| cosocle | D5×D13 | C23×C3 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C2 | |
432 conjugacy classes of subgroups.
| transitive degree | μt(G) = 130 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽13)×D5⋊AGL(1,𝔽5), D3×AGL(1,𝔽5)×AGL(1,𝔽13) |
| maximal quotient of | AGL(1,𝔽13)×D5⋊AGL(1,𝔽5), D3×AGL(1,𝔽5)×AGL(1,𝔽13) |
| holomorph of | C2×C5×C13 |
Past the SmallGroups library coverage — no SmallGroups id.