Finite Group DatabasebetaFinite Group Databasebeta| order | 6144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C210 |
| direct product | C2×C4×#87588⋊C2 |
| Fitting | C23×C4×#120 ⋊ D3 |
| derived | C22⋊(C22⋊A4) ⋊ C23×C4 |
At least 17236 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 4 generators on 18 points:
(4,6,5)(11,16,14,15,17,12)(13,18);(3,4,6,5)(13,14)(15,16);(7,9,10,8);(1,2)(7,8,10,9)240 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((4,6,5)(11,16,14,15,17,12)(13,18), (3,4,6,5)(13,14)(15,16), (7,9,10,8), (1,2)(7,8,10,9));