Finite Group DatabasebetaFinite Group Databasebeta| order | 29645 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×C121⋊C5 |
| unambiguous semidirect product | C121⋊(C5×C49) |
| unambiguous semidirect product | (C49×C121)⋊C5 |
| Fitting, Hall | C49×C121 ⋊ C5 |
| derived, Sylow | C121 ⋊ C5×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | C121⋊C5 |
| commutator, hypocenter | C121 | C5×C49 |
| Frattini, socle | C7×C11 | C7×C11⋊C5 |
| Fitting | C49×C121 | C5 |
| prime radical | C7×C121⋊C5 | C7 |
| cosocle | C7×C121 | C5×C7 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C49 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5929 |
1421 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29645, 2);