Finite Group DatabasebetaFinite Group Databasebeta| order | 20242 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D349⋊C29 |
| unambiguous semidirect product | (C349⋊C29)⋊C2 |
| Fitting, socle, derived, Sylow | C349 ⋊ C2×C29 |
| Hall | C349⋊C29 ⋊ C2 |
| Hall | D349 ⋊ C29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C349 | C2×C29 |
| LCS | G ▷ C349 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 349 |
Polycyclic presentation:
2,29,349|c^a=c^348,c^b=c^25764 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20242, 1);