Finite Group DatabasebetaFinite Group Databasebeta| order | 30324 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#16864560 |
| derived, Sylow | C192 ⋊ C3×C4×C7 |
| Hall | C7×C19×Dic19 ⋊ C3 |
| Hall | C7×#11762245 ⋊ C4 |
| Hall | C7×C192 ⋊ C3×C4 |
| Hall | C19×Dic19 ⋊ C3×C7 |
| Hall | #11762245 ⋊ C4×C7 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 532 |
1050 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30324, 69);