Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #103 |
| Sylow | C5 ⋊ #816 |
| Sylow | C3 ⋊ #4009 |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 16 points:
(1,2,3,5,4)(7,8)(9,11,14,10)(12,15,13,16);(2,3,4,5)(6,7,8)(9,10,12,15,14,11,13,16)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=e,c^2=e,d^2=e,b^a=bd,g^a=g^2,c^b=ce,d^b=de,f^b=f^2,g^c=g^439 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#204, #11751661, AGL(1,𝔽5)×Dic12, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#204, #11751661, AGL(1,𝔽5)×Dic12, … |
| maximal quotient of | #11746493, #11746495, #11746500, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 230);