Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | Aut(G) = C22×S5 (order 480) · Inn(G) = C2×S5 · Out(G) = C2 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C2 | C2×S5 |
| commutator, cosocle, hypocenter | SL(2,𝔽5) | C22 |
| Fitting, hypercenter | C22 | S5 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2 ◁ C22 | |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 48 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 48 points:
(1,3,34,39,8,9,32,25)(2,27,12,41,6,18,19,40)(4,29,38,47,5,28,37,46)(7,10,48,13,14,11,35,21)(15,22,31,42,16,23,33,44)(17,43,20,24,26,45,30,36);(1,47,15,9,48,10)(2,41,13,5,42,14)(3,35,11,8,46,16)(4,44,7,6,40,21)(12,30,45,18,29,31)(17,25,34,36,38,23)(19,20,43,27,28,33)(22,26,39,32,24,37)18 conjugacy classes — view the full character table.
| maximal subgroup of | #11756675, #11756677, #11756678, … |
| maximal normal subgroup of | #11756675, #11756677, #11756678, … |
| maximal quotient of | #11751509, #11751510, #11751511, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 953);