Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #6715 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×C5×M16 ⋊ C2 |
| Hall | C3×C5 ⋊ #104 |
| Sylow | C5 ⋊ #825 |
| Sylow | C3 ⋊ #3957 |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 16 points:
(1,2,4,5,3)(6,7,8)(9,11,12,10,13,14,16,15);(2,3)(4,5)(7,8)(9,10)(11,16)(12,14)(13,15)Polycyclic presentation:
2^5,3,5|b^2=c,c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^2,g^a=g^4,d^b=de84 conjugacy classes — view the full character table.
| maximal subgroup of | #11748206, #11748207, #11748208, … |
| maximal normal subgroup of | #11748206, #11748207, #11748208, … |
| maximal quotient of | #11746285, #11746286, #11746288, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 185);