Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #123 |
| Sylow | C5 ⋊ #929 |
| Sylow | C3 ⋊ #4081 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D3×D5 |
| commutator, socle, cosocle | C22×C3×C5 | C23 |
| Fitting | C23×C3×C5 | C22 |
| prime radical | C2×C5×#67 | C2 |
| hypercenter | C23 | D3×D5 |
| hypocenter | C3×C5 | #123 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C23 | |
156 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,4,5,3)(6,7,8)(15,19)(17,20);(7,8)(10,12)(13,15)(14,17)(16,19)(18,20);(2,3)(4,5)(9,10)(11,12)(13,14,16,18)(15,17,19,20)Polycyclic presentation:
2^5,3,5|a^2=e,b^a=bd,g^a=g^4,c^b=ce,f^b=f^266 conjugacy classes — view the full character table.
| maximal subgroup of | #11747133, #11749183, #11752803, … |
| maximal normal subgroup of | #11747133, #11749183, #11752803, … |
| maximal quotient of | #11748381, #11748383, #11748385, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 615);