Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #984 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×C5⋊S4 |
| commutator, cosocle, hypocenter | C5×SL(2,𝔽3) | C22 |
| Fitting | C5×#41 | D3 |
| socle | C2×C5 | C2×S4 |
| prime radical | C5×#41⋊C3 | C2 |
| hypercenter | C4 | C5⋊S4 |
| LCS | G ▷ C5×SL(2,𝔽3) | |
| UCS | C1 ◁ C2 ◁ C4 | |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 2 generators on 37 points:
(1,12,18,14,4,28,6,29,16,3,17,30)(2,19,24,11,8,31,10,25,22,7,23,32)(5,13,15,27)(9,20,21,26)(33,34,36,37,35);(1,2,6,10)(3,11,14,7)(4,9,17,21)(5,8,15,23)(12,26,29,20)(13,25,27,19)(16,24,18,22)(28,31,30,32)(34,35)(36,37)Polycyclic presentation:
2^2,3,5,2^3|a^2=g,b^2=g,e^2=g,f^2=g,b^a=bg,c^a=c^2,d^a=d^4,e^a=f,f^a=e,e^c=fg,f^c=ef,f^e=fg41 conjugacy classes — view the full character table.
| maximal subgroup of | #11751619, #11751622, #11751628, … |
| maximal normal subgroup of | #11751619, #11751622, #11751628, … |
| maximal quotient of | #11752105, #11752107, C4⋊(C5⋊#226), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1030);