Finite Group DatabasebetaFinite Group Databasebeta| order | 1890 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C27 · Schur multiplier (H2) = C1 |
| direct product | C5×D7⋊C27 |
| unambiguous semidirect product | D7⋊(C5×C27) |
| unambiguous semidirect product | (C5×D7)⋊C27 |
| unambiguous semidirect product | (C7⋊C27)⋊(C2×C5) |
| derived, Sylow | C7 ⋊ C2×C5×C27 |
| Hall | C5×C7⋊C27 ⋊ C2 |
| Hall | C7⋊C27 ⋊ C2×C5 |
| Hall | C5×D7 ⋊ C27 |
| Hall | C5×C7 ⋊ C2×C27 |
| Hall | D7 ⋊ C5×C27 |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 945 |
A minimal faithful permutation representation — 2 generators on 39 points:
(1,2,3,4,5)(7,11,10,8,9,12)(13,18,30,21,33,32,35,14,23,16,26,36,29,38,17,20,19,31,22,34,39,15,25,24,28,27,37);(6,7,10,11,9,12,8)315 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1890, 1);