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) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C4 | S5 |
| commutator, cosocle, hypocenter | SL(2,𝔽5) | C22 |
| Frattini, socle | C2 | C2×S5 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C4 | |
67 conjugacy classes of subgroups.
| minimal degree | μ(G) = 48 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 48 points:
(1,27,31,14,22,4,42,23,15,37,5,28,39,26,38,12,43,40,6,48)(2,35,18,11,29,7,46,32,21,30,8,36,33,3,44,16,47,45,10,17)(9,19,20,34)(13,24,25,41);(1,44,20,18,42,11)(2,48,25,23,46,15)(3,5,29,9,33,43)(4,17,34,32,28,21)(6,8,37,13,40,47)(7,22,41,39,36,26)(10,12,30,19,45,27)(14,16,38,24,31,35)24 conjugacy classes — view the full character table.
| maximal subgroup of | #11751490, #11751492, C2×#91870, … |
| maximal normal subgroup of | #11751490, #11751492, C2×#91870, … |
| maximal quotient of | C4×#6728, C4×#6729, #11751511, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 946);