Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #90938 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C5 ⋊ Q32 |
| Sylow | C5 ⋊ #829 |
| Sylow | C3 ⋊ Dic40 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #6653 |
| commutator, Fitting, cosocle | C3×C5×C8 | C22 |
| Frattini, hypercenter | C8 | D3×D5 |
| socle, prime radical | C2×C3×C5 | D8 |
| hypocenter | C3×C5 | Q32 |
| LCS | G ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 2 generators on 40 points:
(1,2,4,5,3)(7,8)(9,11,20,36,13,22,26,28,14,23,31,40,25,37,12,21)(10,15,24,34,17,29,32,35,18,30,39,38,27,33,16,19);(2,3)(4,5)(6,7,8)(9,10,14,18)(11,19,23,35)(12,24,26,39)(13,27,25,17)(15,28,30,21)(16,31,32,20)(22,38,37,34)(29,36,33,40)Polycyclic presentation:
2^5,3,5|a^2=e,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×Dic40, #11746830, #11746836, … |
| maximal normal subgroup of | D3×Dic40, #11746830, #11746836, … |
| maximal quotient of | #11745898, #11745901, #11745941, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 23);