Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #135 |
| Sylow | C5 ⋊ #950 |
| Sylow | C3 ⋊ #4065 |
124 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,4,5,3)(6,7,8)(9,11,13,17)(10,15,14,23)(12,21,22,19)(16,24,20,18);(7,8)(9,10,13,14)(11,18,17,24)(12,20,22,16)(15,21,23,19);(2,3)(4,5)(10,14)(11,17)(16,20)(19,21)Polycyclic presentation:
2^5,3,5|b^2=e,c^2=e,d^2=e,b^a=be,c^a=ce,g^a=g^4,c^b=cd,d^b=de,f^b=f^2,d^c=de48 conjugacy classes — view the full character table.
| maximal subgroup of | #11751977, #11751978, #11751981, … |
| maximal normal subgroup of | #11751977, #11751978, #11751981, … |
| maximal quotient of | #11747143, #11747145, #11747166, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 592);