Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×#41 ⋊ D3 |
| derived | C5×SL(2,𝔽3) ⋊ C22 |
| Sylow | C5 ⋊ #986 |
| 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 |
| hypercenter | C4 | C5⋊S4 |
| LCS | G ▷ C5×SL(2,𝔽3) | |
| UCS | C1 ◁ C2 ◁ C4 | |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,7,12,6,3,15,5,13,10,2,11,16)(4,8,9,14)(17,18,20,21,19);(2,6)(3,4)(7,14)(8,13)(9,11)(10,12)(18,19)(20,21)Polycyclic presentation:
2^2,3,5,2^3|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 | #11751620, #11751621, #11751626, … |
| maximal normal subgroup of | #11751620, #11751621, #11751626, … |
| maximal quotient of | #11752110, C4⋊(C5⋊GL(2,𝔽3)), #11752113, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1032);