Finite Group DatabasebetaFinite Group Databasebeta| order | 58800 |
| isoclinism | isoclinic class of PSL(2,𝔽49) |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C2 |
| projective special linear | PSL(2,𝔽49) |
| projective symplectic | PSp(2,𝔽49) |
| omega | Ω−(4,𝔽7) |
| projective special unitary | PSU(2,𝔽49) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | G | C1 |
| LCS | G | |
| UCS | C1 | |
51 conjugacy classes of subgroups.
Permutation generators:
(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)(43,44,45,46,47,48,49);(2,5,6,3,4,7,50)(8,24,14,39,18,17,42)(9,32,46,48,29,13,37)(10,12,26,49,21,45,22)(11,31,23,38,36,25,30)(15,20,35,27,47,28,33)(16,41,40,19,44,34,43);(1,8,15,22,29,36,43)(2,9,16,23,30,37,44)(3,10,17,24,31,38,45)(4,11,18,25,32,39,46)(5,12,19,26,33,40,47)(6,13,20,27,34,41,48)(7,14,21,28,35,42,49);(2,35,39,49,46,34,36)(3,28,42,22,13,41,11)(4,33,8,10,37,40,31)(5,27,18,21,48,43,25)(6,47,17,45,29,16,30)(7,15,24,12,9,19,23)(14,26,32,44,38,50,20)27 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((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)(43,44,45,46,47,48,49), (2,5,6,3,4,7,50)(8,24,14,39,18,17,42)(9,32,46,48,29,13,37)(10,12,26,49,21,45,22)(11,31,23,38,36,25,30)(15,20,35,27,47,28,33)(16,41,40,19,44,34,43), (1,8,15,22,29,36,43)(2,9,16,23,30,37,44)(3,10,17,24,31,38,45)(4,11,18,25,32,39,46)(5,12,19,26,33,40,47)(6,13,20,27,34,41,48)(7,14,21,28,35,42,49), (2,35,39,49,46,34,36)(3,28,42,22,13,41,11)(4,33,8,10,37,40,31)(5,27,18,21,48,43,25)(6,47,17,45,29,16,30)(7,15,24,12,9,19,23)(14,26,32,44,38,50,20));