Finite Group DatabasebetaFinite Group Databasebeta| order | 5376 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C27 |
| direct product | AGL(1,𝔽7)×#1891 |
| Fitting | C7×#1891 ⋊ C2×C3 |
| Hall | D7×#1891 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C2×#1891 |
| Sylow | C7 ⋊ C2×C3×#1891 |
3740 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 4 generators on 23 points:
(2,6,5,3,4,7);(1,2,5,6,4,7,3)(13,19)(20,23);(8,10,11,16,12,17,18,22)(9,13,14,20,15,19,21,23);(8,9)(10,13)(11,14)(12,15)(16,20)(17,19)(18,21)(22,23)224 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,6,5,3,4,7), (1,2,5,6,4,7,3)(13,19)(20,23), (8,10,11,16,12,17,18,22)(9,13,14,20,15,19,21,23), (8,9)(10,13)(11,14)(12,15)(16,20)(17,19)(18,21)(22,23));