Finite Group DatabasebetaFinite Group Databasebeta| order | 30240 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26 |
| direct product | D32×AGL(1,𝔽5)×AGL(1,𝔽7) |
| Fitting, socle, derived | C32×C5×C7 ⋊ C23×C3×C4 |
| Hall | C32×C5×ΓL(1,𝔽8) ⋊ C23×C4 |
| Hall | C32×ΓL(1,𝔽8) ⋊ C23×AGL(1,𝔽5) |
| Hall | C5×C7 ⋊ C2×C3×C4×D32 |
| Sylow | C7 ⋊ C2×C3×D32×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×D32×AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5×C7 | C23×C3×C4 |
| prime radical | D32×D5×AGL(1,𝔽7) | C2 |
| cosocle | C32×C7×D5 | C24×C3 |
| LCS | G ▷ C32×C5×C7 | |
| UCS | C1 | |
4488 conjugacy classes of subgroups.
315 conjugacy classes. The character table is too large to display.
| automorphism group of | D15×D21, D3×D105, D21⋊D15 |
| holomorph of | C5×D3×C7 |
Past the SmallGroups library coverage — no SmallGroups id.