Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×#4183 |
| Fitting | C2×D4×AΣL(1,𝔽27) ⋊ C2 |
| Sylow | AΣL(1,𝔽27) ⋊ C22×D4 |
2360 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 2360 conjugacy classes of subgroups — too many to draw. Only its 211 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 4 generators on 15 points:
(3,4,5,6)(7,14,15,10,8,11,9,12,13);(1,2)(8,12,14)(11,13,15);(8,11)(9,10)(12,15)(13,14);(4,6)130 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((3,4,5,6)(7,14,15,10,8,11,9,12,13), (1,2)(8,12,14)(11,13,15), (8,11)(9,10)(12,15)(13,14), (4,6));