Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C4×C52×ΓL(1,𝔽8) |
| unambiguous semidirect product | (C4×C7)⋊(C3×C52) |
| unambiguous semidirect product | (C4×C5×C7)⋊(C3×C5) |
| Fitting, Hall | C4×C52×C7 ⋊ C3 |
| derived, Sylow | C7 ⋊ C3×C4×C52 |
| Hall | C52×C7 ⋊ C3×C4 |
| Hall | C4×C7 ⋊ C3×C52 |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 700 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,4)(5,6,7,8,9)(16,17,18)(19,21,20);(10,11,12,13,14)(15,16,17,19,18,20,21)500 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 55);