Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×D15⋊Q8 |
| Hall | C3×C5 ⋊ C22×Q8 |
| Sylow | C5 ⋊ C2×D3×Q8 |
| Sylow | C3 ⋊ C2×Q8×D5 |
312 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 4 generators on 18 points:
(3,4,5)(6,7,9,10,8)(11,14,15,18)(12,16,13,17);(1,2)(4,5)(11,13,15,12)(14,16,18,17);(7,8)(9,10)(11,12,15,13)(14,17,18,16);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | #11747490, #11747491, #11747496, … |
| maximal normal subgroup of | #11747490, #11747491, #11747496, … |
| maximal quotient of | #11752463, #11752467, #11752471, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1082);