Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#889 |
| Hall | C3×C5 ⋊ #125 |
| Sylow | C3 ⋊ C5×#125 |
112 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 62 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) = 480 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(5,9)(8,11)(12,14,15,18)(13,16,17,19)(20,21,22,23,24);(4,6,7,10)(5,8,9,11)(14,18)(16,19);(2,3)(4,5)(6,8)(7,9)(10,11)(12,13,15,17)(14,16,18,19)120 conjugacy classes — view the full character table.
| maximal subgroup of | #11753307, #11753308, #11753310, … |
| maximal normal subgroup of | #11753307, #11753308, #11753310, … |
| maximal quotient of | C5×#4647, C5×#4650, C5×#4652, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 768);