Finite Group DatabasebetaFinite Group Databasebeta| order | 30492 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C11 |
| direct product | C7×Dic3×C112⋊C3 |
| unambiguous semidirect product | C3⋊(C4×C7×C112⋊C3) |
| unambiguous semidirect product | (C112×Dic3)⋊(C3×C7) |
| derived | C3×C112 ⋊ C3×C4×C7 |
| Hall | C3×C7×C112⋊C3 ⋊ C4 |
| Hall | C3×C112⋊C3 ⋊ C4×C7 |
| Hall | C7×C112 ⋊ C3×Dic3 |
| Sylow | C112 ⋊ C3×C7×Dic3 |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2772 |
1806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 240);