Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C4×A4×AGL(1,ℤ/9) |
| Fitting | C22×C4×3−1+2 ⋊ C2×C3 |
| derived | C22×C9 ⋊ C2×C32×C4 |
559 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 559 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 108 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,5,9,3,2,4,8,7,6)(10,11,12,13)(15,16,17);(2,6,7,4,5,9)(3,8)(14,17)(15,16)160 conjugacy classes — view the full character table.
| maximal subgroup of | A4×AGL(1,𝔽5)×AGL(1,ℤ/9), C4×S4×AGL(1,ℤ/9) |
| maximal normal subgroup of | C4×S4×AGL(1,ℤ/9) |
| maximal quotient of | A4×AGL(1,𝔽5)×AGL(1,ℤ/9) |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,5,9,3,2,4,8,7,6)(10,11,12,13)(15,16,17), (2,6,7,4,5,9)(3,8)(14,17)(15,16));