Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C22 |
| direct product | 3−1+2×GL(2,ℤ/4) |
| Fitting | C24×3−1+2 ⋊ D3 |
606 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 606 conjugacy classes of subgroups — too many to draw. Only its 84 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:
(1,3,4)(6,8)(9,12,17,11,15,13,14,10,16);(2,3)(5,6)(7,8)(10,12,15)(13,17,16)154 conjugacy classes — view the full character table.
| maximal subgroup of | 3−1+2×A4⋊S4 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,3,4)(6,8)(9,12,17,11,15,13,14,10,16), (2,3)(5,6)(7,8)(10,12,15)(13,17,16));