Finite Group DatabasebetaFinite Group Databasebeta| order | 246 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C5×C8 (order 80) · Inn(G) = C1 · Out(G) = C2×C5×C8 |
| holomorph | G ⋊ Aut(G) = C2×D3×AGL(1,𝔽41) |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C246 |
| abelian | C2×C3×C41 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 246 |
A minimal faithful permutation representation — 1 generator on 46 points:
(1,2)(3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46)246 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(246, 4);