Finite Group DatabasebetaFinite Group Databasebeta| order | 4800 |
| isoclinism | isoclinic class of #1043 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C43 · Schur multiplier (H2) = C43 |
| direct product | C3×C42×#1043 |
| Fitting | C3×C42×C52 ⋊ C4 |
| derived, Sylow | C52 ⋊ C3×C43 |
| Hall | C3×C52 ⋊ C43 |
2064 conjugacy classes of subgroups; only the 468 normal subgroups are shown.
This group has 2064 conjugacy classes of subgroups — too many to draw. Only its 468 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 1200 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,3)(9,10,13,11,12)(18,19,20,21);(5,6,7,8)(10,11,12,13);(4,5,8,6,7)(14,15,16,17)480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C42×D3×#1043, C3×#127×#1043, #874×#1043, … |
| maximal normal subgroup of | C42×D3×#1043, C3×#127×#1043, #874×#1043, … |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3)(9,10,13,11,12)(18,19,20,21), (5,6,7,8)(10,11,12,13), (4,5,8,6,7)(14,15,16,17));