Finite Group DatabasebetaFinite Group Databasebeta| order | 30492 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3×C11 |
| direct product | C3×Dic7×C112⋊C3 |
| derived, Hall | C7×C112 ⋊ C32×C4 |
| Hall | C3×C7×C112⋊C3 ⋊ C4 |
| Hall | C112×Dic7 ⋊ C32 |
| Sylow | C112 ⋊ C32×Dic7 |
| Sylow | C7 ⋊ C3×C4×C112⋊C3 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2772 |
1290 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 237);