Finite Group DatabasebetaFinite Group Databasebeta| order | 29524 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D61×D121 |
| unambiguous semidirect product | (C61×D121)⋊C2 |
| unambiguous semidirect product | (C121×D61)⋊C2 |
| unambiguous semidirect product | D7381⋊C2 |
| Fitting, derived, Hall | C61×C121 ⋊ C22 |
| Sylow | C121 ⋊ C2×D61 |
| Sylow | C61 ⋊ C2×D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C61×C121 | C22 |
| Frattini | C11 | D11×D61 |
| socle | C11×C61 | C2×D11 |
| LCS | G ▷ C61×C121 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7381 |
1984 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29524, 8);