Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C24 |
| direct product | 3−1+2×#953 |
| Fitting | C24×C3×3−1+2 ⋊ C2 |
| Sylow | C3×3−1+2 ⋊ #120 |
1777 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 1777 conjugacy classes of subgroups — too many to draw. Only its 287 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
330 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72220063, #72220105, 3−1+2×#5032, … |
| maximal normal subgroup of | #72220105, 3−1+2×#5032, #72220141 |
| maximal quotient of | #72220063 |
Past the SmallGroups library coverage — no SmallGroups id.