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 ⋊ #912 |
| 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)(10,15)(12,20)(14,21)(16,17)(18,24)(22,23);(7,8)(9,11,13,19)(10,14,17,23)(12,18,20,24)(15,21,16,22);(2,3)(4,5)(9,10)(11,14)(12,15)(13,17)(16,20)(18,21)(19,23)(22,24)Polycyclic presentation:
2^5,3,5|b^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 | D5×#912, #11754050, #11754055, … |
| maximal normal subgroup of | D5×#912, #11754050, #11754055, … |
| maximal quotient of | #11747148, #11747176, #11747208, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 569);