Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #117 |
| Sylow | C5 ⋊ #877 |
| Sylow | C3 ⋊ #4023 |
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)(14,18)(15,19);(7,8)(9,11,12,10)(13,15,16,19)(14,17,18,20);(2,3)(4,5)(9,10,12,11)(13,14)(15,17)(16,18)(19,20)Polycyclic presentation:
2^5,3,5|a^2=d,b^2=de,c^a=ce,g^a=g^4,c^b=ce,f^b=f^266 conjugacy classes — view the full character table.
| maximal subgroup of | #11747131, #11749174, #11752781, … |
| maximal normal subgroup of | #11747131, #11749174, #11752781, … |
| maximal quotient of | #11748331, #11748332, #11748338, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 608);