Finite Group DatabasebetaFinite Group Databasebeta| order | 34522 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C421 · Schur multiplier (H2) = C1 |
| direct product | D41×C421 |
| unambiguous semidirect product | C41⋊(C2×C421) |
| Fitting, socle, Hall | C41×C421 ⋊ C2 |
| derived, Sylow | C41 ⋊ C2×C421 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C421 | D41 |
| commutator, cosocle, hypocenter | C41 | C2×C421 |
| Frattini | C1 | G |
| Fitting, socle | C41×C421 | C2 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C421 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17261 |
9262 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34522, 1);