Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C24×C32 |
| direct product | C2×3−1+2×C22⋊A4 |
| Fitting | C25×3−1+2 ⋊ C3 |
| Sylow | C25 ⋊ C3×3−1+2 |
1492 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 148 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C22⋊A4×AGL(1,ℤ/9) |
| maximal normal subgroup of | C2×C22⋊A4×AGL(1,ℤ/9) |
| maximal quotient of | C2×3−1+2×#997, 3−1+2×#5950, C2×C22⋊A4×C9⋊C9 |
Past the SmallGroups library coverage — no SmallGroups id.