Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #6715 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C5 ⋊ #108 |
| Sylow | C5 ⋊ #822 |
| Sylow | C3 ⋊ #3954 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,4,5,3)(6,7,8)(9,11,12,20,14,21,13,22)(10,15,16,19,18,23,17,24);(2,3)(4,5)(7,8)(9,10,13,17,14,18,12,16)(11,19,20,23,21,24,22,15)Polycyclic presentation:
2^5,3,5|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bd,f^a=f^2,g^a=g^4,d^b=de84 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#822, D3×#3954, #11748171, … |
| maximal normal subgroup of | D5×#822, D3×#3954, #11748171, … |
| maximal quotient of | #11746300, #11746301, #11746379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 182);