Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of Dic30 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C3×C42×C5 ⋊ C2 |
| Hall | C3×C5 ⋊ #117 |
| Sylow | C5 ⋊ #872 |
| Sylow | C3 ⋊ #4018 |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,4,5,3)(6,7,8)(9,10,11,12)(14,18)(17,20);(13,15,16,19)(14,17,18,20);(2,3)(4,5)(7,8)(13,14)(15,17)(16,18)(19,20)Polycyclic presentation:
2^5,3,5|b^2=e,c^2=d,c^a=ce,f^a=f^2,g^a=g^4132 conjugacy classes — view the full character table.
| maximal subgroup of | #11746860, #11746938, #11746939, … |
| maximal normal subgroup of | #11746860, #11746938, #11746939, … |
| maximal quotient of | #11750751, #11750752, #11750753, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 837);