Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #1201 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ C4⋊C8 |
| Sylow | C5 ⋊ Dic3⋊C8 |
| Sylow | C3 ⋊ #3946 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C4 | D3×D5 |
| commutator | C2×C3×C5 | C2×C8 |
| Fitting, cosocle | C2×C3×C4×C5 | C22 |
| socle, prime radical | C22×C3×C5 | C2×C4 |
| hypocenter | C3×C5 | C4⋊C8 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,4,5,3)(7,8)(10,12)(13,15,16,20,17,14,18,19);(2,3)(4,5)(6,7,8)(9,10)(11,12)(13,14,16,19,17,15,18,20)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=c,c^2=e,b^a=bd,g^a=g^4,f^b=f^284 conjugacy classes — view the full character table.
| maximal subgroup of | #11746851, #11746852, #11746855, … |
| maximal normal subgroup of | #11746851, #11746852, #11746855, … |
| maximal quotient of | #11745865, #11745868, #11745928, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 59);