Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #6652 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C5 ⋊ #108 |
| Sylow | C5 ⋊ #822 |
| Sylow | C3 ⋊ #3954 |
60 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)(9,11,12,19,14,20,13,22)(10,15,16,23,17,24,21,18);(2,3)(4,5)(6,7,8)(9,10,12,16,14,17,13,21)(11,18,19,15,20,23,22,24)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=c,c^2=e,d^2=e,b^a=bd,d^a=de,g^a=g^4,d^b=de,f^b=f^260 conjugacy classes — view the full character table.
| maximal subgroup of | #11747106, #11747107, #11748060, … |
| maximal normal subgroup of | #11747106, #11747107, #11748060, … |
| maximal quotient of | #11745865, #11745868, #11745982, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 68);