Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×#686 |
| Fitting | C2×C3×C5×D4 ⋊ C2 |
| Hall | C3×C5 ⋊ C2×D8 |
| Sylow | C5 ⋊ C2×C3×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)(6,7,9,10,8)(12,15)(13,18)(16,17);(7,8)(9,10)(11,12)(13,15)(14,17)(16,18);(1,2)102 conjugacy classes — view the full character table.
| maximal subgroup of | #11748947, #11748981, #11748982, … |
| maximal normal subgroup of | #11748947, #11748981, #11748982, … |
| maximal quotient of | C2×C3×#3939, C2×C3×#3941, C3×#65256, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 724);