Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#951 |
| Hall | C3×C5 ⋊ #137 |
| Sylow | C3 ⋊ C5×#137 |
120 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 120 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)(6,13)(7,15)(9,16)(11,12)(17,18)(20,21,22,23,24);(4,6)(5,9)(7,14)(8,13)(10,18)(11,16)(12,17)(15,19);(2,3)(4,5,8,12)(6,9,13,17)(7,10,15,11)(14,18,19,16)105 conjugacy classes — view the full character table.
| maximal subgroup of | #11749415, #11749425, #11749448, … |
| maximal normal subgroup of | #11749415, #11749425, #11749448, … |
| maximal quotient of | C5×#4995, C5×#4996, C5×#5004, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 830);