Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#915 |
| Fitting | C3×C5×SD16 ⋊ C2 |
| Hall | C3×C5 ⋊ #137 |
| Sylow | C3 ⋊ C5×#137 |
120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(5,10)(6,12)(7,15)(9,16)(13,14)(17,19)(20,21,22,23,24);(4,6,8,14)(5,9,10,17)(7,12,15,13)(11,19,18,16);(2,3)(4,5)(6,9)(7,11)(8,10)(12,19)(13,16)(14,17)(15,18)90 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#915, #11754070, #11754072, … |
| maximal normal subgroup of | D5×#915, #11754070, #11754072, … |
| maximal quotient of | C5×#4757, C5×#4759, C5×#4765, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 794);