Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(C23⋊#1035) |
| unambiguous semidirect product | C23⋊(C9⋊#1035) |
| Fitting, derived, Hall | C9×C23×C25 ⋊ C4 |
| Hall | C23×C25 ⋊ Dic9 |
| Hall | C9×C25 ⋊ Dic23 |
| Hall | C9×C23 ⋊ #1035 |
| Sylow | C25 ⋊ Dic207 |
| Sylow | C23 ⋊ C9⋊#1035 |
| Sylow | C9 ⋊ C23⋊#1035 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C23×C25 | C4 |
| Frattini | C3×C5 | C3⋊(C23⋊AGL(1,𝔽5)) |
| socle | C3×C5×C23 | ΓL(1,𝔽16) |
| prime radical | C3×C23×D25 | D3 |
| cosocle | C9×C23×D25 | C2 |
| LCS | G ▷ C9×C23×C25 | |
| UCS | C1 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5175 |
Polycyclic presentation:
2^2,3,5,23,3,5|a^2=b,c^3=f^2,d^5=g,c^a=c^2f,d^a=d^2g,e^a=e^22,f^a=f^2,g^a=g^2,d^b=d^4g^4,g^b=g^41452 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20700, 13);