Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #90939 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ D16 |
| Sylow | C5 ⋊ D48 |
| Sylow | C3 ⋊ #3958 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #6654 |
| 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)(10,14)(11,18)(12,19)(15,16)(17,22)(20,24)(21,23);(2,3)(4,5)(6,7,8)(9,10,11,15,19,23,24,22,13,17,20,21,12,16,18,14)Polycyclic presentation:
2^5,3,5|a^2=c,c^2=de,d^2=e,b^a=bc,g^a=g^4,c^b=cd,d^b=de,f^b=f^257 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D48, #11746816, #11746817, … |
| maximal normal subgroup of | D5×D48, #11746816, #11746817, … |
| maximal quotient of | #11745820, #11745825, #11745826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 15);