Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ C4⋊Q8 |
| Sylow | C5 ⋊ #869 |
| Sylow | C3 ⋊ #4015 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D15 |
| commutator, socle, prime radical, cosocle | C22×C3×C5 | C23 |
| Fitting | C3×C42×C5 | C2 |
| hypercenter | C42 | D15 |
| hypocenter | C3×C5 | C4⋊Q8 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C42 | |
136 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,4,5,3)(6,7,8)(9,10,11,12);(13,15,16,20)(14,17,18,19);(2,3)(4,5)(7,8)(10,12)(13,14,16,18)(15,19,20,17)Polycyclic presentation:
2^5,3,5|a^2=e,b^2=e,c^2=d,b^a=be,c^a=cd,f^a=f^2,g^a=g^4126 conjugacy classes — view the full character table.
| maximal subgroup of | #11745859, #11745860, #11745863, … |
| maximal normal subgroup of | #11745859, #11745860, #11745863, … |
| maximal quotient of | #11750757, #11750762, #11750781, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 834);