Finite Group DatabasebetaFinite Group Databasebeta| order | 15120 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | D32×D5×AGL(1,𝔽7) |
| Fitting, socle, derived | C32×C5×C7 ⋊ C24×C3 |
| Hall | C32×C5×ΓL(1,𝔽8) ⋊ C24 |
| Hall | C32×ΓL(1,𝔽8) ⋊ C23×D5 |
| Hall | C5×C7 ⋊ C22×C3×D32 |
| Sylow | C7 ⋊ C2×C3×D32×D5 |
| Sylow | C5 ⋊ C2×D32×AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C5×C7 | C24×C3 |
| LCS | G ▷ C32×C5×C7 | |
| UCS | C1 | |
2568 conjugacy classes of subgroups.
252 conjugacy classes — view the full character table.
| maximal subgroup of | D32×AGL(1,𝔽5)×AGL(1,𝔽7) |
| maximal normal subgroup of | D32×AGL(1,𝔽5)×AGL(1,𝔽7) |
Past the SmallGroups library coverage — no SmallGroups id.