Finite Group DatabasebetaFinite Group Databasebeta| order | 23820 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#22547261 |
| Fitting, socle, derived, Hall | C3×C5×C397 ⋊ C4 |
| Hall | C5×C397 ⋊ Dic3 |
| Hall | C3×C397 ⋊ Dic5 |
| Sylow | C397 ⋊ Dic15 |
| Hall | C3×C5 ⋊ #13097544 |
| Sylow | C5 ⋊ C3⋊#13097544 |
| Sylow | C3 ⋊ #22547261 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C397 | C4 |
| prime radical, cosocle | C3×C5×D397 | C2 |
| LCS | G ▷ C3×C5×C397 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5955 |
Polycyclic presentation:
2^2,3,5,397|a^2=b,c^a=c^2,d^a=d^4,e^a=e^63,e^b=e^3961503 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23820, 37);