Finite Group DatabasebetaFinite Group Databasebeta| order | 2520 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×D5×C3⋊AGL(1,𝔽7) |
| Fitting, socle | C2×C3×C5×C7 ⋊ C22×C3 |
| derived | C3×C5×C7 ⋊ C23×C3 |
| Hall | C3×C5×ΓL(1,𝔽8) ⋊ C23 |
| Hall | C3×ΓL(1,𝔽8) ⋊ C22×D5 |
| Hall | C5×C7 ⋊ C22×C3×D3 |
| Sylow | C7 ⋊ C2×C3×D3×D5 |
| Sylow | C5 ⋊ C22×C3⋊AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×C3⋊AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C3×C5×C7 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C7 | C22×C3 |
| LCS | G ▷ C3×C5×C7 | |
| UCS | C1 ◁ C2 | |
276 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
96 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.