Finite Group DatabasebetaFinite Group Databasebeta| order | 20286 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊#11725077 |
| derived, Hall | C72×C23 ⋊ C2×C9 |
| Hall | C23×#89204 ⋊ C2 |
| Hall | C7⋊D161 ⋊ C9 |
| Hall | #89204 ⋊ D23 |
| Sylow | C72 ⋊ C9×D23 |
| Sylow | C23 ⋊ #11725077 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C23⋊#64424 |
| commutator, hypocenter | C72×C23 | C2×C9 |
| Fitting, socle, cosocle | C3×C72×C23 | C2×C3 |
| prime radical | C3×C7⋊D161 | C3 |
| LCS | G ▷ C72×C23 | |
| UCS | C1 ◁ C3 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10143 |
Polycyclic presentation:
2,3,7^2,23,3|b^3=f,c^a=c^6,d^a=d^6,e^a=e^22,c^b=c^2,d^b=d^2669 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20286, 38);