Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #6715 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C5×C4⋊C4 ⋊ C2 |
| Hall | C3×C5 ⋊ #102 |
| Sylow | C5 ⋊ #809 |
| Sylow | C3 ⋊ #3941 |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,4,5,3)(6,7,8)(9,10,11,12)(14,17)(15,20)(18,19);(2,3)(4,5)(7,8)(13,14)(15,17)(16,19)(18,20)Polycyclic presentation:
2^5,3,5|b^2=c,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 | #11747138, #11747145, #11747159, … |
| maximal normal subgroup of | #11747138, #11747145, #11747159, … |
| maximal quotient of | #11746272, #11746303, #11746304, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 169);