Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of SL(2,𝔽5) |
| automorphism | Aut(G) = C22×S5 (order 480) · Inn(G) = A5 · Out(G) = C23 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| direct product | C4×SL(2,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C2×C4 | A5 |
| commutator, hypocenter | SL(2,𝔽5) | C4 |
| Frattini, socle, cosocle | C22 | C2×A5 |
| prime radical | C2×SL(2,𝔽5) | C2 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2×C4 | |
55 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 28 points:
(5,7,10)(6,9,14)(8,12,16)(11,15,20)(13,17,21)(18,22,19)(23,25,27)(24,26,28);(1,2,3,4)(5,6,8,11)(7,10,12,16)(9,13,15,19)(14,18,20,17)(21,23,22,24)(25,27,26,28)36 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 222);