Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #124 |
| Sylow | C5 ⋊ #947 |
| Sylow | C3 ⋊ #4021 |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,4,5,3)(6,7,8)(13,15,16,20)(14,18,17,19);(7,8)(9,10,11,12)(14,17)(18,19);(2,3)(4,5)(10,12)(13,14,16,17)(15,19,20,18)Polycyclic presentation:
2^5,3,5|a^2=e,b^2=de,c^2=e,b^a=bd,c^a=ce,g^a=g^4,f^b=f^272 conjugacy classes — view the full character table.
| maximal subgroup of | #11746559, #11747377, #11747378, … |
| maximal normal subgroup of | #11746559, #11747377, #11747378, … |
| maximal quotient of | #11746910, #11746911, #11746921, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 450);