Finite Group DatabasebetaFinite Group Databasebeta| order | 34556 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D53×D163 |
| unambiguous semidirect product | (D53×C163)⋊C2 |
| unambiguous semidirect product | (C53×D163)⋊C2 |
| unambiguous semidirect product | D8639⋊C2 |
| Fitting, socle, derived, Hall | C53×C163 ⋊ C22 |
| Sylow | C163 ⋊ C2×D53 |
| Sylow | C53 ⋊ C2×D163 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C53×C163 | C22 |
| LCS | G ▷ C53×C163 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8639 |
2324 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34556, 8);