Finite Group DatabasebetaFinite Group Databasebeta| order | 29524 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D671 |
| unambiguous semidirect product | (C11×D11)⋊D61 |
| unambiguous semidirect product | (D11×C61)⋊D11 |
| Fitting, socle, derived, Hall | C112×C61 ⋊ C22 |
| Sylow | C112 ⋊ C2×D61 |
| Sylow | C61 ⋊ D112 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C61 | C22 |
| LCS | G ▷ C112×C61 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1342 |
2359 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29524, 26);