Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×D5×Dic6 |
| Hall | C3×C5 ⋊ C22×Q8 |
| Sylow | C5 ⋊ C22×Dic6 |
| Sylow | C3 ⋊ C2×Q8×D5 |
312 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 132 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)(11,13,14,18)(12,15,16,17);(1,2)(4,5)(11,12,14,16)(13,17,18,15);(7,8)(9,10);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#810, #11747487, #11747492, … |
| maximal normal subgroup of | D5×#810, #11747487, #11747492, … |
| maximal quotient of | #11752465, #11752469, #11752473, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1073);