Finite Group DatabasebetaFinite Group Databasebeta| order | 30240 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23 |
| direct product | AGL(1,𝔽7)×D5⋊AGL(1,𝔽9) |
| Fitting, socle, derived | C32×C5×C7 ⋊ C22×C3×C8 |
| Hall | C32×C5×ΓL(1,𝔽8) ⋊ C22×C8 |
| Hall | C32×ΓL(1,𝔽8) ⋊ C2×D5⋊C8 |
| Hall | C5×C7 ⋊ C22×C3×AGL(1,𝔽9) |
| Sylow | C7 ⋊ C2×C3×D5⋊AGL(1,𝔽9) |
| Sylow | C5 ⋊ C2×AGL(1,𝔽7)×AGL(1,𝔽9) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5×C7 | C22×C3×C8 |
| prime radical | D5×C3⋊D3×AGL(1,𝔽7) | C4 |
| cosocle | C7×#4379 | C23×C3 |
| LCS | G ▷ C32×C5×C7 | |
| UCS | C1 | |
776 conjugacy classes of subgroups.
168 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×AGL(1,𝔽7)×AGL(1,𝔽9) |
| maximal normal subgroup of | AGL(1,𝔽5)×AGL(1,𝔽7)×AGL(1,𝔽9) |
Past the SmallGroups library coverage — no SmallGroups id.