Finite Group DatabasebetaFinite Group Databasebeta| order | 23772 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C283 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)⋊C4×C283 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C4×C283) |
| unambiguous semidirect product | Dic7⋊(C3×C283) |
| derived, Sylow | C7 ⋊ C3×C4×C283 |
| Hall | Dic7×C283 ⋊ C3 |
| Hall | ΓL(1,𝔽8)×C283 ⋊ C4 |
| Hall | C7×C283 ⋊ C3×C4 |
| Hall | Dic7 ⋊ C3×C283 |
| Hall | ΓL(1,𝔽8) ⋊ C4×C283 |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7924 |
3962 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23772, 18);