Finite Group DatabasebetaFinite Group Databasebeta| order | 3120 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C4 |
| direct product | AGL(1,𝔽5)×AGL(1,𝔽13) |
| Fitting, socle, derived, Hall | C5×C13 ⋊ C3×C42 |
| Hall | AGL(1,𝔽5)×#261 ⋊ C3 |
| Hall | C5×C13⋊C3 ⋊ C42 |
| Hall | C13⋊C3 ⋊ C4×AGL(1,𝔽5) |
| Sylow | C13 ⋊ C3×C4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×AGL(1,𝔽13) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C13 | C3×C42 |
| prime radical | D5×D13⋊C3 | C22 |
| cosocle | D5×D13 | C22×C3 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 | |
120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
65 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.