Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D5×#216 |
| Hall | C3×C5 ⋊ C2×Q16 |
| Sylow | C5 ⋊ C2×#216 |
| Sylow | C3 ⋊ D5×Q16 |
120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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)(4,6,8,14)(5,9,11,18)(7,16,17,13)(10,19,15,12)(20,21,23,24,22);(2,3)(4,5,8,11)(6,12,14,19)(7,15,17,10)(9,16,18,13);(21,22)(23,24)48 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#216, #11751968, #11751969, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#216, #11751968, #11751969, … |
| maximal quotient of | #11747139, #11747140, #11747169, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 583);