Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of SL(2,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C22×SL(2,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, socle, hypercenter | C23 | A5 |
| commutator, hypocenter | SL(2,𝔽5) | C22 |
| Frattini, cosocle | C2 | C22×A5 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C23 | |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 28 points:
(1,2)(3,4)(5,7,11)(6,9,14)(8,13,19)(10,15,20)(12,17,22)(16,21,18)(23,25,27)(24,26,28);(3,4)(5,6,8,12)(7,10,13,18)(9,14,17,22)(11,16,19,15)(20,23,21,24)(25,27,26,28)36 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 960);