Finite Group DatabasebetaFinite Group Databasebeta| order | 20160 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | D5×AGL(1,𝔽7)×GL(2,𝔽3) |
| Fitting | C5×C7×Q8 ⋊ C22×C3×D3 |
| derived | C5×C7×SL(2,𝔽3) ⋊ C23×C3 |
| Hall | C5×C7 ⋊ C22×C3×GL(2,𝔽3) |
| Sylow | C7 ⋊ C2×C3×D5×GL(2,𝔽3) |
| Sylow | C5 ⋊ C2×AGL(1,𝔽7)×GL(2,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×S4×AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C5×C7×SL(2,𝔽3) | C23×C3 |
| Fitting | C5×C7×Q8 | C22×C3×D3 |
| socle | C2×C5×C7 | C22×C3×S4 |
| LCS | G ▷ C5×C7×SL(2,𝔽3) | |
| UCS | C1 ◁ C2 | |
1788 conjugacy classes of subgroups.
224 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.