Finite Group DatabasebetaFinite Group Databasebeta| order | 15372 |
| isoclinism | isoclinic class of C3⋊AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×C3⋊(ΓL(1,𝔽8)⋊C4) |
| unambiguous semidirect product | C3⋊(C61×ΓL(1,𝔽8)⋊C4) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(Dic3×C61) |
| unambiguous semidirect product | Dic21⋊(C3×C61) |
| derived | C3×C7 ⋊ C3×C4×C61 |
| Hall | C3×ΓL(1,𝔽8)×C61 ⋊ C4 |
| Hall | C7×C61 ⋊ C3×Dic3 |
| Hall | C3×ΓL(1,𝔽8) ⋊ C4×C61 |
| Sylow | C7 ⋊ C3×Dic3×C61 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5124 |
1464 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15372, 96);