Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3×C5 |
| direct product | C4×C3⋊D3×C5⋊D5 |
| Fitting | C32×C4×C52 ⋊ C22 |
| derived, Hall | C32×C52 ⋊ C22×C4 |
| Sylow | C52 ⋊ C2×C4×C3⋊D3 |
| Sylow | C32 ⋊ C2×C4×C5⋊D5 |
1296 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 228 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:
(1,2,3,4)(10,11,13,14,12)(18,19,20);(6,7)(8,9)(11,12)(13,14)(15,16,17);(5,6,8,9,7)(16,17)(19,20)336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C3⋊D3×#1043, C2×C4×C3⋊D3×C5⋊D5, D4×C3⋊D3×C5⋊D5, … |
| maximal normal subgroup of | C4×C3⋊D3×#1043, C2×C4×C3⋊D3×C5⋊D5, D4×C3⋊D3×C5⋊D5, … |
| maximal quotient of | C2×C4×C3⋊D3×C5⋊D5 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3,4)(10,11,13,14,12)(18,19,20), (6,7)(8,9)(11,12)(13,14)(15,16,17), (5,6,8,9,7)(16,17)(19,20));