Finite Group DatabasebetaFinite Group Databasebeta| order | 2520 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | D3×C7×ΓL(1,𝔽16) |
| Fitting, socle, Hall | C32×C5×C7 ⋊ C2×C4 |
| derived, Hall | C32×C5 ⋊ C2×C4×C7 |
| Hall | C32×C7 ⋊ C2×AGL(1,𝔽5) |
| Hall | C5×C7 ⋊ D3×Dic3 |
| Sylow | C32 ⋊ C2×C7×AGL(1,𝔽5) |
| Sylow | C5 ⋊ D3×C7×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D3×ΓL(1,𝔽16) |
| commutator, hypocenter | C32×C5 | C2×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C7 | C2×C4 |
| prime radical | C3×D3×C7×D5 | C2 |
| cosocle | C32×D5 | C22×C7 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C7 | |
140 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
189 conjugacy classes — view the full character table.
| maximal subgroup of | D3×ΓL(1,𝔽8)×ΓL(1,𝔽16), D32×C7×AGL(1,𝔽5), D3×D21⋊AGL(1,𝔽5), … |
| maximal normal subgroup of | D3×ΓL(1,𝔽8)×ΓL(1,𝔽16), D32×C7×AGL(1,𝔽5), D3×D21⋊AGL(1,𝔽5), … |
Past the SmallGroups library coverage — no SmallGroups id.