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 ⋊ #944 |
| Sylow | C3 ⋊ #4090 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D3×D5 |
| commutator, socle, prime radical, cosocle | C22×C3×C5 | C23 |
| Fitting | C2×C3×C4×C5 | C22 |
| hypercenter | C2×C4 | D3×D5 |
| hypocenter | C3×C5 | C4⋊Q8 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
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)(13,16,17,20)(14,18,15,19);(7,8)(10,12)(13,15,17,14)(16,18,20,19);(2,3)(4,5)(9,10)(11,12)(13,14,17,15)(16,19,20,18)Polycyclic presentation:
2^5,3,5|a^2=e,b^2=e,c^2=e,b^a=bd,c^a=ce,g^a=g^4,c^b=ce,f^b=f^260 conjugacy classes — view the full character table.
| maximal subgroup of | #11746560, #11747426, #11747427, … |
| maximal normal subgroup of | #11746560, #11747426, #11747427, … |
| maximal quotient of | #11746947, #11746962, #11746968, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 461);