Finite Group DatabasebetaFinite Group Databasebeta| order | 15372 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#19103976 |
| derived, Hall | C7×C61 ⋊ C32×C4 |
| Hall | C3×#13046196 ⋊ C4 |
| Hall | Dic427 ⋊ C32 |
| Sylow | C61 ⋊ C3×ΓL(1,𝔽8)⋊C4 |
| Sylow | C7 ⋊ C3×Dic61⋊C3 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5124 |
462 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15372, 84);