Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#950 |
| Fitting | C3×C5×#41 ⋊ C2 |
| Hall | C3×C5 ⋊ #135 |
| Sylow | C3 ⋊ C5×#135 |
124 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 58 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)(7,15)(9,16)(11,12)(13,19)(17,18)(20,21,22,23,24);(4,6,8,14)(5,9,12,18)(7,13,15,19)(10,16,11,17);(2,3)(4,5)(6,9)(7,10)(8,12)(11,15)(13,16)(14,18)(17,19)120 conjugacy classes — view the full character table.
| maximal subgroup of | #11749432, #11749433, #11749442, … |
| maximal normal subgroup of | #11749432, #11749433, #11749442, … |
| maximal quotient of | C5×#4996, C5×#4998, C5×#5002, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 829);