Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#878 |
| Hall | C3×C5 ⋊ C22⋊Q8 |
| Sylow | C3 ⋊ C5×C22⋊Q8 |
148 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3)(5,7)(8,10,11,15)(9,12,13,14)(16,17,18,19,20);(4,5)(6,7);(2,3)(8,9,11,13)(10,14,15,12)120 conjugacy classes — view the full character table.
| maximal subgroup of | #11752781, #11752784, #11752785, … |
| maximal normal subgroup of | #11752781, #11752784, #11752785, … |
| maximal quotient of | C5×#4646, C5×#4647, C5×#4654, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 757);