Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of D3×AGL(1,𝔽5) |
| automorphism | Aut(G) = C2×C4×D3×AGL(1,𝔽5) (order 960) · Inn(G) = D3×AGL(1,𝔽5) · Out(G) = C2×C4 |
| 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 | C4 | D3×AGL(1,𝔽5) |
| commutator, hypocenter | C3×C5 | C2×C16 |
| Fitting | C3×C4×C5 | C2×C4 |
| socle | C2×C3×C5 | C2×C8 |
| prime radical | C2×D15 | C8 |
| cosocle | C3×#168 | C22 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C4 | |
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:
(1,2,3,5,4)(7,8)(9,11,13,20,14,12,19,21)(10,15,17,23,18,16,22,24);(2,3,4,5)(6,7,8)(9,10,12,16,13,17,21,24,14,18,11,15,19,22,20,23)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=d,c^2=d,d^2=e,g^a=g^2,f^b=f^2,g^c=g^460 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D5⋊C16, #11751642, #11751644, … |
| maximal normal subgroup of | D3×D5⋊C16, #11751642, #11751644, … |
| maximal quotient of | #11746481, #11746483, #11746541, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 240);