Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×C5×#213 |
| Fitting | C2×C3×C5×D4 ⋊ C2 |
| Hall | C3×C5 ⋊ C2×D8 |
| Sylow | C3 ⋊ C2×C5×D8 |
152 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 152 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) = 18 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 18 points:
(3,4,5)(6,7,8,9,10)(12,15)(13,18)(16,17);(4,5)(11,12)(13,15)(14,17)(16,18);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | Dic5×#213, #11748974, #11748977, … |
| maximal normal subgroup of | Dic5×#213, #11748974, #11748977, … |
| maximal quotient of | C2×C5×#807, C2×C5×#809, C5×#4967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 810);