Finite Group DatabasebetaFinite Group Databasebeta| order | 29645 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×#10597243 |
| Fitting, Hall | C112×C49 ⋊ C5 |
| derived, Sylow | C112 ⋊ C5×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | #10597243 |
| commutator, hypocenter | C112 | C5×C49 |
| Frattini | C7 | C7×#10597243 |
| Fitting | C112×C49 | C5 |
| socle, cosocle | C7×C112 | C5×C7 |
| prime radical | C7×#10597243 | C7 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C49 | |
84 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, 6);