Finite Group DatabasebetaFinite Group Databasebeta| order | 18396 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C73 · Schur multiplier (H2) = C1 |
| direct product | C73×C3⋊(ΓL(1,𝔽8)⋊C4) |
| unambiguous semidirect product | C3⋊(C73×ΓL(1,𝔽8)⋊C4) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(Dic3×C73) |
| unambiguous semidirect product | Dic21⋊(C3×C73) |
| derived | C3×C7 ⋊ C3×C4×C73 |
| Hall | C3×ΓL(1,𝔽8)×C73 ⋊ C4 |
| Hall | C7×C73 ⋊ C3×Dic3 |
| Hall | C3×ΓL(1,𝔽8) ⋊ C4×C73 |
| Sylow | C7 ⋊ C3×Dic3×C73 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6132 |
1752 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18396, 108);