Finite Group DatabasebetaFinite Group Databasebeta| order | 29682 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D97⋊C9 |
| unambiguous semidirect product | D97⋊(C9×C17) |
| unambiguous semidirect product | (C97⋊C9)⋊(C2×C17) |
| unambiguous semidirect product | (C17×D97)⋊C9 |
| derived, Sylow | C97 ⋊ C2×C9×C17 |
| Hall | C17×C97⋊C9 ⋊ C2 |
| Hall | C17×D97 ⋊ C9 |
| Hall | C17×C97 ⋊ C2×C9 |
| Hall | C97⋊C9 ⋊ C2×C17 |
| Hall | D97 ⋊ C9×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C17 | D97⋊C3 |
| commutator, hypocenter | C97 | C2×C9×C17 |
| Frattini | C3 | C17×D97⋊C3 |
| Fitting, socle | C3×C17×C97 | C2×C3 |
| prime radical | C3×C17×D97 | C3 |
| cosocle | C3×C97 | C2×C3×C17 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C3×C17 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14841 |
1122 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29682, 10);