Finite Group DatabasebetaFinite Group Databasebeta| order | 17892 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C71 · Schur multiplier (H2) = C3 |
| derived, Sylow | C7 ⋊ C32×C4×C71 |
| Hall | C3×ΓL(1,𝔽8)×C71 ⋊ C4 |
| Hall | Dic7×C71 ⋊ C32 |
| Hall | C7×C71 ⋊ C32×C4 |
| Hall | C3×ΓL(1,𝔽8) ⋊ C4×C71 |
| Hall | Dic7 ⋊ C32×C71 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5964 |
2982 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17892, 52);