Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #6728 |
| automorphism | Aut(G) = C22×S5 (order 480) · Inn(G) = S5 · Out(G) = C22 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived | SL(2,𝔽5) ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, Fitting, socle, hypercenter | C22 | S5 |
| commutator, hypocenter | SL(2,𝔽5) | C4 |
| prime radical, cosocle | C2×SL(2,𝔽5) | C2 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 | |
47 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 44 points:
(1,2)(3,4)(6,7,9)(8,11,15)(12,17,25)(13,19,29)(14,16,23)(18,27,37)(20,30,39)(21,31,22)(26,32,33)(28,35,42)(34,40,36)(38,43,41);(1,3,2,4)(5,6,8,12,18,28)(7,10,14,21,32,41)(9,13,20)(11,16,24,34,37,29)(15,22)(17,26,36)(19,23,33,25,35,39)(27,38)(30,31,40,44,42,43)24 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#6728, C4×#6729, #11751505, … |
| maximal normal subgroup of | C4×#6728, C4×#6729, #11751505, … |
| maximal quotient of | SL(2,𝔽5)⋊C8, C2×#91143, C3×#91143, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 219);