Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #126 |
| Sylow | C5 ⋊ #879 |
| Sylow | C3 ⋊ #4025 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D3×D5 |
| commutator, socle, cosocle | C22×C3×C5 | C23 |
| Fitting, prime radical | C23×C3×C5 | C22 |
| hypercenter | C23 | D3×D5 |
| hypocenter | C3×C5 | #126 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C23 | |
120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,4,5,3)(6,7,8)(11,15)(13,16)(18,22)(21,24);(7,8)(9,11)(10,13)(12,15)(14,16)(17,19,20,23)(18,21,22,24);(2,3)(4,5)(9,10,12,14)(11,13,15,16)(17,18,20,22)(19,21,23,24)Polycyclic presentation:
2^5,3,5|a^2=d,b^2=e,c^a=ce,g^a=g^4,c^b=cde,f^b=f^260 conjugacy classes — view the full character table.
| maximal subgroup of | #11752777, #11752778, #11752782, … |
| maximal normal subgroup of | #11752777, #11752778, #11752782, … |
| maximal quotient of | #11748583, #11748592, #11748616, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 607);