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 ⋊ #935 |
| Sylow | C3 ⋊ #4081 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D15 |
| commutator, socle, cosocle | C22×C3×C5 | C23 |
| Fitting, prime radical | C2×C3×C5×D4 | C2 |
| hypercenter | C2×D4 | D15 |
| hypocenter | C3×C5 | #123 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
156 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 55 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)(10,12)(15,19)(17,20);(13,15)(14,17)(16,19)(18,20);(2,3)(4,5)(7,8)(9,10)(11,12)(13,14,16,18)(15,17,19,20)Polycyclic presentation:
2^5,3,5|a^2=e,c^a=cd,f^a=f^2,g^a=g^4,c^b=ce84 conjugacy classes — view the full character table.
| maximal subgroup of | #11746004, #11746005, #11746293, … |
| maximal normal subgroup of | #11746004, #11746005, #11746293, … |
| maximal quotient of | #11751044, #11751045, #11751047, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 900);