Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| isoclinism | isoclinic class of #87856 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C32×C22⋊#1043 |
| Fitting | C22×C32×C52 ⋊ C4 |
| Hall | C32×C52 ⋊ C22⋊C4 |
| Sylow | C52 ⋊ C32×C22⋊C4 |
816 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 192 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) = 900 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3)(8,10)(12,13,14,15)(17,18,19,20);(4,5,6)(7,8)(9,10)(16,17,20,18,19);(11,12,15,13,14)306 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D4×#1043, C3⋊D3×C22⋊#1043, #72230625, … |
| maximal normal subgroup of | C32×D4×#1043, C3⋊D3×C22⋊#1043, #72230625, … |
| maximal quotient of | C2×C32×C22⋊#1043 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3)(8,10)(12,13,14,15)(17,18,19,20), (4,5,6)(7,8)(9,10)(16,17,20,18,19), (11,12,15,13,14));