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 ⋊ #919 |
| Sylow | C3 ⋊ #4096 |
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)(9,12,14,20)(10,16,17,24)(11,18,13,22)(15,23,21,19);(7,8)(9,11,14,13)(10,15,17,21)(12,18,20,22)(16,23,24,19);(2,3)(4,5)(9,10,14,17)(11,15,13,21)(12,19,20,23)(16,22,24,18)Polycyclic presentation:
2^5,3,5|a^2=e,b^2=e,c^2=e,d^2=e,c^a=cd,d^a=de,g^a=g^4,f^b=f^2,d^c=de51 conjugacy classes — view the full character table.
| maximal subgroup of | #11754075, #11754079, #11754090, … |
| maximal normal subgroup of | #11754075, #11754079, #11754090, … |
| maximal quotient of | #11747148, #11747174, #11747210, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 595);