Finite Group DatabasebetaFinite Group Databasebeta| order | 7560 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33×C5 · Schur multiplier (H2) = C2×C33 |
| direct product | C3×C5×A4×AGL(1,𝔽7) |
| Fitting, socle | C22×C3×C5×C7 ⋊ C2×C32 |
| derived | C22×C7 ⋊ C2×C33×C5 |
| Hall | C22×C5×D7 ⋊ C33 |
| Hall | C22×D7 ⋊ C33×C5 |
| Hall | C5×C7 ⋊ C2×C32×A4 |
| Sylow | C7 ⋊ C2×C32×C5×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | A4×AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C22×C7 | C2×C33×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C5×C7 | C2×C32 |
| LCS | G ▷ C22×C7 | |
| UCS | C1 ◁ C3×C5 | |
544 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 152 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.
Past the SmallGroups library coverage — no SmallGroups id.