Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #90939 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C5 ⋊ SD32 |
| Sylow | C5 ⋊ #800 |
| Sylow | C3 ⋊ #3960 |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,4,5,3)(7,8)(9,11,14,10)(12,20,17,23)(13,16,21,19)(15,22,18,24);(2,3)(4,5)(6,7,8)(9,10,12,15,21,19,24,20,14,11,17,18,13,16,22,23)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=e,c^2=de,d^2=e,b^a=bce,g^a=g^4,c^b=cd,d^b=de,f^b=f^257 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#800, #11746817, #11746827, … |
| maximal normal subgroup of | D5×#800, #11746817, #11746827, … |
| maximal quotient of | #11745896, #11745900, #11745942, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 21);