Finite Group DatabasebetaFinite Group Databasebeta| order | 3360 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | AGL(1,𝔽7)×#685 |
| Fitting | C2×C4×C5×C7 ⋊ C22×C3 |
| Hall | D7×#685 ⋊ C3 |
| Hall | C5×ΓL(1,𝔽8) ⋊ C2×C22⋊C4 |
| Hall | C5×C7 ⋊ C2×C3×C22⋊C4 |
| Hall | ΓL(1,𝔽8) ⋊ C2×#685 |
| Sylow | C7 ⋊ C2×C3×#685 |
| Sylow | C5 ⋊ C22⋊C4×AGL(1,𝔽7) |
528 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
182 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C22⋊C4×AGL(1,𝔽7), AGL(1,𝔽7)×#4083, AGL(1,𝔽7)×#4028 |
| maximal normal subgroup of | D5×C22⋊C4×AGL(1,𝔽7), AGL(1,𝔽7)×#4083, AGL(1,𝔽7)×#4028 |
Past the SmallGroups library coverage — no SmallGroups id.