Finite Group DatabasebetaFinite Group Databasebeta| order | 16884 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C67 · Schur multiplier (H2) = C3 |
| direct product | C3×C67×ΓL(1,𝔽8)⋊C4 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C3×C4×C67) |
| unambiguous semidirect product | Dic7⋊(C32×C67) |
| unambiguous semidirect product | (C3×Dic7)⋊(C3×C67) |
| derived, Sylow | C7 ⋊ C32×C4×C67 |
| Hall | C3×ΓL(1,𝔽8)×C67 ⋊ C4 |
| Hall | Dic7×C67 ⋊ C32 |
| Hall | C7×C67 ⋊ C32×C4 |
| Hall | C3×ΓL(1,𝔽8) ⋊ C4×C67 |
| Hall | Dic7 ⋊ C32×C67 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5628 |
2814 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16884, 71);