Finite Group DatabasebetaFinite Group Databasebeta| order | 15372 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×Dic7⋊C9 |
| unambiguous semidirect product | Dic7⋊(C9×C61) |
| unambiguous semidirect product | (C7⋊C9)⋊(C4×C61) |
| derived, Sylow | C7 ⋊ C4×C9×C61 |
| Hall | C61×C7⋊C9 ⋊ C4 |
| Hall | Dic7×C61 ⋊ C9 |
| Hall | C7×C61 ⋊ C4×C9 |
| Hall | C7⋊C9 ⋊ C4×C61 |
| Hall | Dic7 ⋊ C9×C61 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15372 |
2562 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15372, 18);