Finite Group DatabasebetaFinite Group Databasebeta| order | 15552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32 |
| direct product | C3×#67×PSU(3,𝔽2)⋊C3 |
| Fitting | C22×C34 ⋊ C2×SL(2,𝔽3) |
2583 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 19 points:
(4,5,6)(8,10)(11,12,14)(13,18,19)(15,17,16);(1,2,3)(5,6)(7,8)(9,10)(12,18,16,13)(14,15,17,19)270 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((4,5,6)(8,10)(11,12,14)(13,18,19)(15,17,16), (1,2,3)(5,6)(7,8)(9,10)(12,18,16,13)(14,15,17,19));