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, hypercenter | C2 | D5×S4 |
| commutator, cosocle, hypocenter | C5×SL(2,𝔽3) | C22 |
| Fitting | C5×Q8 | C2×D3 |
| socle | C2×C5 | C2×S4 |
| prime radical | C5⋊(#41⋊C3) | C2 |
| LCS | G ▷ C5×SL(2,𝔽3) | |
| UCS | C1 ◁ C2 | |
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:
(1,12,16,27,6,29,18,13)(2,19,22,26,10,25,24,20)(3,17,28,5,14,4,30,15)(7,23,31,9,11,8,32,21)(33,34,36,37,35);(1,2,6,10)(3,11,14,7)(4,21,16,23,15,24,17,9,18,8,5,22)(12,20,28,19,27,31,29,26,30,25,13,32)(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,d^a=d^4,c^b=c^2,e^b=f,f^b=e,e^c=fg,f^c=ef,f^e=fg29 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#91891, #11756761, #11756765, … |
| maximal normal subgroup of | C2×#91891, #11756761, #11756765, … |
| maximal quotient of | #11751590, #11751591, #11751593, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 967);