Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #90938 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ D16 |
| Sylow | C5 ⋊ #826 |
| Sylow | C3 ⋊ D80 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #6653 |
| commutator, Fitting, cosocle | C3×C5×C8 | C22 |
| Frattini, hypercenter | C8 | D3×D5 |
| socle | C2×C3×C5 | D8 |
| hypocenter | C3×C5 | D16 |
| LCS | G ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
56 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)(9,10,15,21,12,16,19,22,13,17,23,24,18,20,11,14);(2,3)(4,5)(6,7,8)(10,14)(11,15)(12,18)(16,24)(17,22)(19,23)(20,21)Polycyclic presentation:
2^5,3,5|b^2=cd,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,g^a=g^4,f^b=f^266 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D80, #11746820, #11746821, … |
| maximal normal subgroup of | D3×D80, #11746820, #11746821, … |
| maximal quotient of | #11745819, #11745823, #11745824, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 14);