Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #1201 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#6667 |
| Hall | C3×C5 ⋊ C2×C22⋊C4 |
| Sylow | C5 ⋊ C2×(C2×D3)⋊C4 |
| Sylow | C3 ⋊ C2×#685 |
264 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 92 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:
(1,2)(4,5)(6,7,8,9)(11,13)(14,15,17,18,16);(3,4,5)(7,9)(10,11,12,13)(15,16)(17,18);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #11746567, #11748574, #11748577, … |
| maximal normal subgroup of | #11746567, #11748574, #11748577, … |
| maximal quotient of | C2×#90957, #11748349, #11748350, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 616);