Finite Group DatabasebetaFinite Group Databasebeta| order | 20842 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D613⋊C17 |
| unambiguous semidirect product | (C613⋊C17)⋊C2 |
| Fitting, socle, derived, Sylow | C613 ⋊ C2×C17 |
| Hall | C613⋊C17 ⋊ C2 |
| Hall | D613 ⋊ C17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C613 | C2×C17 |
| LCS | G ▷ C613 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 613 |
Polycyclic presentation:
2,17,613|c^a=c^612,c^b=c^58652 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20842, 1);