Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #125 |
| Sylow | C5 ⋊ #870 |
| Sylow | C3 ⋊ #4016 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D15 |
| commutator, socle, prime radical, cosocle | C22×C3×C5 | C23 |
| Fitting | C3×C42×C5 | C2 |
| hypercenter | C42 | D15 |
| hypocenter | C3×C5 | #125 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C42 | |
112 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,4,5,3)(6,7,8)(10,14)(13,16)(17,19,20,23)(18,22,21,24);(9,11,12,15)(10,13,14,16)(18,21)(22,24);(2,3)(4,5)(7,8)(9,10)(11,13)(12,14)(15,16)(17,18,20,21)(19,22,23,24)Polycyclic presentation:
2^5,3,5|a^2=e,b^2=d,c^2=e,b^a=be,c^a=cd,f^a=f^2,g^a=g^4126 conjugacy classes — view the full character table.
| maximal subgroup of | #11745851, #11746286, #11746888, … |
| maximal normal subgroup of | #11745851, #11746286, #11746888, … |
| maximal quotient of | #11750758, #11750761, #11751029, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 835);