Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #90939 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C5 ⋊ Q32 |
| Sylow | C5 ⋊ Dic24 |
| Sylow | C3 ⋊ #3961 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #6654 |
| 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)(9,11,14,22)(10,15,18,29)(12,23,26,39)(13,27,24,21)(16,30,33,40)(17,34,31,28)(19,35,36,32)(20,37,38,25);(2,3)(4,5)(6,7,8)(9,10,12,16,24,31,37,35,14,18,26,33,13,17,25,32)(11,19,20,34,27,40,39,29,22,36,38,28,21,30,23,15)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=e,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×Dic24, #11746827, #11746828, … |
| maximal normal subgroup of | D5×Dic24, #11746827, #11746828, … |
| maximal quotient of | #11745900, #11745902, #11745939, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 24);