Finite Group DatabasebetaFinite Group Databasebeta| order | 30492 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2×C11 |
| direct product | C22×C7⋊(C112⋊C9) |
| derived, Hall | C7×C112 ⋊ C22×C9 |
| Hall | C22×C7×C112 ⋊ C9 |
| Hall | C22×C112 ⋊ C7⋊C9 |
| Sylow | C112 ⋊ C22×C7⋊C9 |
| Hall | C22×C7 ⋊ C112⋊C9 |
| Sylow | C7 ⋊ C22×C112⋊C9 |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2772 |
3420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 204);