Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C4 |
| direct product | #127×D27⋊C3 |
| Fitting | #127×C27⋊C3 ⋊ C2 |
| Sylow | C27⋊C3 ⋊ C2×#127 |
2100 conjugacy classes of subgroups; only the 340 normal subgroups are shown.
This group has 2100 conjugacy classes of subgroups — too many to draw. Only its 340 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
294 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.