Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #6654 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#6654 |
| Hall | C3×C5 ⋊ C2×D8 |
| Sylow | C5 ⋊ C2×D24 |
| Sylow | C3 ⋊ C2×#686 |
152 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 52 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)(6,7,9,10,8)(12,15)(13,18)(16,17);(3,4,5)(7,8)(9,10)(11,12,13,16,14,17,18,15);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#6654, #11747025, #11747029, … |
| maximal normal subgroup of | C4×#6654, #11747025, #11747029, … |
| maximal quotient of | #11746906, #11746912, #11746955, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 378);