Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C23×C33 |
| direct product | C3×C9×#997 |
| Fitting | C3×C9×H(5,𝔽2) ⋊ C3 |
| derived, Sylow | H(5,𝔽2) ⋊ C32×C9 |
790 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 790 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 216 |
A minimal faithful permutation representation — 3 generators on 20 points:
(5,9)(6,11)(12,13,15,14,16,18,17,19,20);(1,2,3)(4,10,7,8)(5,6,9,11);(5,8,6)(9,10,11)297 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72276014, C9⋊C9×#997, #72276184, … |
| maximal normal subgroup of | #72276014, C9⋊C9×#997, #72276184, … |
| maximal quotient of | C9⋊C9×#997 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((5,9)(6,11)(12,13,15,14,16,18,17,19,20), (1,2,3)(4,10,7,8)(5,6,9,11), (5,8,6)(9,10,11));