Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | Aut(G) = C2×#41×AGL(1,𝔽5) (order 640) · Inn(G) = AGL(1,𝔽5) · Out(G) = C2×#41 |
| homology | Abelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×#674 |
| derived, Sylow | C5 ⋊ C2×C3×C16 |
| Hall | C3×C5 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C4 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C2×C3×C16 |
| Frattini | C4 | C2×C3×AGL(1,𝔽5) |
| Fitting | C2×C3×C4×C5 | C4 |
| socle, prime radical | C22×C3×C5 | C8 |
| cosocle | #168 | C22×C3 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C3×C4 | |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 2 generators on 26 points:
(3,4,5)(7,8,9,10)(11,12,13,16,14,17,19,22,15,18,20,23,21,24,25,26);(1,2)(6,7,8,10,9)120 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#674, #11746541, #11746542, … |
| maximal normal subgroup of | Dic3×#674, #11746541, #11746542, … |
| maximal quotient of | C3×C4×#674, C3×C4⋊#674, C2×C3×#3928, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 277);