Finite Group DatabasebetaFinite Group Databasebeta| order | 30324 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C4×C19×#87704 |
| Fitting, Hall | C4×C7×C192 ⋊ C3 |
| derived | C7×C19 ⋊ C3×C4×C19 |
| Hall | C7×C192 ⋊ C3×C4 |
| Hall | C4×C192 ⋊ ΓL(1,𝔽8) |
| Sylow | C192 ⋊ C4×ΓL(1,𝔽8) |
| Hall | C4×C7 ⋊ C19×C19⋊C3 |
| Sylow | C7 ⋊ C4×C19×C19⋊C3 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1596 |
3572 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30324, 123);