Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #1201 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#1204 |
| Hall | C3×C5 ⋊ C4×Q8 |
| Sylow | C5 ⋊ C4×Dic6 |
| Sylow | C3 ⋊ C4×Dic10 |
140 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 66 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) = 480 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,4,5,3)(7,8)(13,15,16,20)(14,17,18,19);(2,3)(4,5)(6,7,8)(13,14,16,18)(15,19,20,17);(9,10,11,12)84 conjugacy classes — view the full character table.
| maximal subgroup of | #11747564, #11747565, #11747566, … |
| maximal normal subgroup of | #11747564, #11747565, #11747566, … |
| maximal quotient of | C8×#1204, #11747819, #11747822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 543);