Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | Aut(G) = D4×S5 (order 960) · Inn(G) = C2×S5 · Out(G) = C22 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived | SL(2,𝔽5) ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C2 | C2×S5 |
| commutator, cosocle, hypocenter | SL(2,𝔽5) | C22 |
| Fitting, hypercenter | C4 | S5 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2 ◁ C4 | |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 40 |
A minimal faithful permutation representation — 2 generators on 40 points:
(1,2,3,6,4,8,7,12)(5,9,14,22,13,20,30,28)(10,17,11,18,21,16,19,29)(15,23,33,25,31,35,38,26)(24,32,39,37,40,34,27,36);(1,12,29,39,40,14)(2,9,31,33,21,3)(4,6,18,27,24,30)(5,22,37,19,17,35)(7,8,20,15,38,10)(11,16,23,13,28,36)(32,34)18 conjugacy classes — view the full character table.
| maximal subgroup of | #11751493, #11751494, #11751521, … |
| maximal normal subgroup of | #11751493, #11751494, #11751521, … |
| maximal quotient of | C4⋊#6729, #11751509, #11751514, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 948);