Finite Group DatabasebetaFinite Group Databasebeta| order | 30492 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C112 · Schur multiplier (H2) = C11 |
| direct product | C3×C112×Dic21 |
| unambiguous semidirect product | C3⋊(C3×C112×Dic7) |
| derived | C3×C7 ⋊ C3×C4×C112 |
| Hall | C32×C7×C112 ⋊ C4 |
| Hall | C32×C112 ⋊ Dic7 |
| Hall | C7×C112 ⋊ C3×Dic3 |
| Hall | C32×C7 ⋊ C4×C112 |
| Sylow | C32 ⋊ C112×Dic7 |
| Sylow | C7 ⋊ C3×C112×Dic3 |
392 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10164 |
8712 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 265);