Finite Group DatabasebetaFinite Group Databasebeta| order | 9360 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C42 · Schur multiplier (H2) = C3×C4 |
| direct product | C3×AGL(1,𝔽5)×AGL(1,𝔽13) |
| Fitting, socle | C3×C5×C13 ⋊ C3×C42 |
| derived, Hall | C5×C13 ⋊ C32×C42 |
| Hall | AGL(1,𝔽5)×#261 ⋊ C32 |
| Hall | C3×C5×C13⋊C3 ⋊ C42 |
| Hall | C3×C13⋊C3 ⋊ C4×AGL(1,𝔽5) |
| Sylow | C13 ⋊ C32×C4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C3×C4×AGL(1,𝔽13) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | AGL(1,𝔽5)×AGL(1,𝔽13) |
| commutator, hypocenter | C5×C13 | C32×C42 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C13 | C3×C42 |
| prime radical | C3×D5×D13⋊C3 | C22 |
| cosocle | D5×D13 | C22×C32 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C3 | |
360 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 195 |
195 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽5)×AGL(1,𝔽13) |
| maximal normal subgroup of | D3×AGL(1,𝔽5)×AGL(1,𝔽13) |
Past the SmallGroups library coverage — no SmallGroups id.