Finite Group DatabasebetaFinite Group Databasebeta| order | 21756 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#15690920 |
| derived | C7×C37 ⋊ C3×C4×C7 |
| Hall | C72×Dic37 ⋊ C3 |
| Hall | C7×#11715913 ⋊ C4 |
| Hall | C72×C37 ⋊ C3×C4 |
| Hall | Dic37 ⋊ C7×ΓL(1,𝔽8) |
| Sylow | C72 ⋊ Dic37⋊C3 |
| Sylow | C37 ⋊ C4×C7×ΓL(1,𝔽8) |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3108 |
728 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21756, 85);