Finite Group DatabasebetaFinite Group Databasebeta| order | 3360 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C26 |
| direct product | C22×D3×C7×AGL(1,𝔽5) |
| Fitting, socle | C22×C3×C5×C7 ⋊ C2×C4 |
| derived, Hall | C3×C5 ⋊ C23×C4×C7 |
| Hall | C3×C5×C7 ⋊ C23×C4 |
| Hall | C5×C7 ⋊ C22×C4×D3 |
| Hall | C3×C7 ⋊ C23×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C22×C4×D3×C7 |
| Sylow | C3 ⋊ C23×C7×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C7 | D3×AGL(1,𝔽5) |
| commutator, hypocenter | C3×C5 | C23×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C5×C7 | C2×C4 |
| prime radical | C22×D3×C7×D5 | C2 |
| cosocle | C3×D5 | C24×C7 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C22×C7 | |
944 conjugacy classes of subgroups; only the 332 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 332 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
420 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C4×D3×C7×AGL(1,𝔽5) |
| maximal normal subgroup of | C2×C4×D3×C7×AGL(1,𝔽5) |
| maximal quotient of | C2×C4×D3×C7×AGL(1,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.