Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #131 |
| Sylow | C5 ⋊ #948 |
| Sylow | C3 ⋊ #4094 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D15 |
| commutator, socle | C2×C3×C5 | C22×C4 |
| Fitting, prime radical | C3×C5×#41 | C2 |
| cosocle | C3×C4×C5 | C23 |
| hypercenter | #41 | D15 |
| hypocenter | C3×C5 | #131 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C4 ◁ #41 | |
124 conjugacy classes of subgroups.
| 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)(11,17)(14,20)(18,23)(21,24);(9,11)(10,14)(12,18)(13,17)(15,21)(16,20)(19,23)(22,24);(2,3)(4,5)(7,8)(9,10,12,15,13,16,19,22)(11,14,18,21,17,20,23,24)Polycyclic presentation:
2^5,3,5|a^2=d,d^2=e,f^a=f^2,g^a=g^4,c^b=ce90 conjugacy classes — view the full character table.
| maximal subgroup of | #11749440, #11749441, #11749442, … |
| maximal normal subgroup of | #11749440, #11749441, #11749442, … |
| maximal quotient of | #11751098, #11751100, #11751101, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 913);