Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of D3×D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Hall | C3×C5 ⋊ C2×C16 |
| Sylow | C5 ⋊ D3×C16 |
| Sylow | C3 ⋊ D5×C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D3×D5 |
| commutator, hypocenter | C3×C5 | C2×C16 |
| Fitting, cosocle | C3×C5×C8 | C22 |
| socle | C2×C3×C5 | C2×C8 |
| prime radical | C2×D15 | C8 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ 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)(9,11,12,18,13,19,20,24,14,10,15,16,21,17,22,23);(2,3)(4,5)(6,7,8)(9,10,12,16,13,17,20,23,14,11,15,18,21,19,22,24)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=c,c^2=d,d^2=e,g^a=g^4,f^b=f^296 conjugacy classes — view the full character table.
| maximal subgroup of | #11746481, #11746483, D3×D5×C16, … |
| maximal normal subgroup of | #11746481, #11746483, D3×D5×C16, … |
| maximal quotient of | #11745814, #11745817, #11745872, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 9);