Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | A4×#611⋊C3 |
| Fitting | C24×3−1+2 ⋊ C2×C3 |
611 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 611 conjugacy classes of subgroups — too many to draw. Only its 81 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:
(2,4,3)(6,8)(9,13,17,11,10,12,16,15,14);(1,4)(2,3)(5,6)(7,8)(10,14,15,12,13,17)(11,16)124 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#63694⋊C3 |
| maximal quotient of | A4×#63694⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,4,3)(6,8)(9,13,17,11,10,12,16,15,14), (1,4)(2,3)(5,6)(7,8)(10,14,15,12,13,17)(11,16));