Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C7 · Schur multiplier (H2) = C25 |
| direct product | C3×C7×#1004 |
| Fitting | C2×C32×C7×D4 ⋊ C2 |
| Hall | C32×C7 ⋊ H(5,𝔽2) |
| Sylow | C32 ⋊ C7×H(5,𝔽2) |
718 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
567 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#10596675, C3×D7×#1004, #72246737, … |
| maximal normal subgroup of | C7×#10596675, C3×D7×#1004, #72246737, … |
Past the SmallGroups library coverage — no SmallGroups id.