Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C24 |
| direct product | C2×#13048167 |
| Sylow | C25 ⋊ C27⋊C3 |
1368 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 1368 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72229223, C2×#72229255, C2×#72229238, … |
| maximal normal subgroup of | C2×#72229223, C2×#72229255, C2×#72229238, … |
Past the SmallGroups library coverage — no SmallGroups id.