Finite Group DatabasebetaFinite Group Databasebeta| order | 21372 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C137 · Schur multiplier (H2) = C1 |
| direct product | C137×Dic13⋊C3 |
| unambiguous semidirect product | Dic13⋊(C3×C137) |
| unambiguous semidirect product | (Dic13×C137)⋊C3 |
| derived, Sylow | C13 ⋊ C3×C4×C137 |
| Hall | Dic13×C137 ⋊ C3 |
| Hall | C13⋊C3×C137 ⋊ C4 |
| Hall | C13×C137 ⋊ C3×C4 |
| Hall | Dic13 ⋊ C3×C137 |
| Hall | C13⋊C3 ⋊ C4×C137 |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7124 |
2192 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21372, 11);