Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of C52⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C5 |
| direct product | C4×C7×C52⋊C3 |
| unambiguous semidirect product | (C4×C52)⋊(C3×C7) |
| Fitting, Hall | C4×C52×C7 ⋊ C3 |
| derived, Sylow | C52 ⋊ C3×C4×C7 |
| Hall | C52×C7 ⋊ C3×C4 |
| Hall | C4×C52 ⋊ C3×C7 |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 420 |
A minimal faithful permutation representation — 2 generators on 26 points:
(1,2,3,4)(5,6,7,8,9,10,11)(12,13,15)(14,18,20)(16,21,24)(17,23,26)(19,22,25);(12,14,19,24,26)(13,18,22,16,17)(15,21,20,23,25)308 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 56);