Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D5×Dic3⋊C4 |
| Hall | C3×C5 ⋊ C2×C4⋊C4 |
| Sylow | C5 ⋊ C2×Dic3⋊C4 |
| Sylow | C3 ⋊ D5×C4⋊C4 |
184 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 16 points:
(1,2,3)(4,5,6,7)(9,11)(12,13,15,16,14);(2,3)(8,9,10,11);(13,14)(15,16)72 conjugacy classes — view the full character table.
| maximal subgroup of | #11751745, #11751747, AGL(1,𝔽5)×Dic3⋊C4, … |
| maximal normal subgroup of | #11751745, #11751747, AGL(1,𝔽5)×Dic3⋊C4, … |
| maximal quotient of | #11747188, #11747189, D5×#807, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 468);