Finite Group DatabasebetaFinite Group Databasebeta| order | 12600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#72218917 |
| Fitting, socle | C3×C52×C7 ⋊ C2×C3×C4 |
| derived, Hall | C52×C7 ⋊ C2×C32×C4 |
| Hall | C3×C52×ΓL(1,𝔽8) ⋊ C2×C4 |
| Hall | #1043⋊D7 ⋊ C32 |
| Hall | C3×ΓL(1,𝔽8) ⋊ D5⋊AGL(1,𝔽5) |
| Sylow | C52 ⋊ C3×C4×AGL(1,𝔽7) |
| Sylow | C7 ⋊ C32×D5⋊AGL(1,𝔽5) |
456 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 210 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(1,𝔽7)×D5⋊AGL(1,𝔽5) |
| maximal normal subgroup of | C3×AGL(1,𝔽7)×D5⋊AGL(1,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.