Finite Group DatabasebetaFinite Group Databasebeta| order | 19200 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
| direct product | D5×#1020⋊AGL(1,𝔽5) |
| Fitting | C24×C52 ⋊ C2×C4×D3 |
| derived | C52×C22⋊A4 ⋊ C22×C4 |
| Sylow | C52 ⋊ C2×#1020⋊C4 |
5526 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 5526 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 18 points:
(2,7,6)(3,8,4)(10,11)(12,13)(14,15)(16,17);(3,4)(5,7)(9,10,12,13,11);(1,2)(3,5)(4,7)(6,8)(15,17,16,18)152 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((2,7,6)(3,8,4)(10,11)(12,13)(14,15)(16,17), (3,4)(5,7)(9,10,12,13,11), (1,2)(3,5)(4,7)(6,8)(15,17,16,18));