Finite Group DatabasebetaFinite Group Databasebeta| order | 4800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C23×C5 |
| direct product | A4×C22⋊#1044 |
| Fitting | C24×C52 ⋊ C3×C4 |
| Hall | C22×C22⋊#1044 ⋊ C3 |
| Sylow | C52 ⋊ A4×C22⋊C4 |
1032 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 1032 conjugacy classes of subgroups — too many to draw. Only its 60 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) = 60 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,2,5,3,4)(6,7,8,10,9)(12,14)(16,17,18);(2,3,4,5)(7,8,9,10)(11,12)(13,14)(15,18)(16,17)136 conjugacy classes — view the full character table.
| maximal subgroup of | A4×A4⋊#1044, A4×#11717375, #72260312, … |
| maximal normal subgroup of | A4×#11717375, #72260312, #72260402 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,5,3,4)(6,7,8,10,9)(12,14)(16,17,18), (2,3,4,5)(7,8,9,10)(11,12)(13,14)(15,18)(16,17));