Finite Group DatabasebetaFinite Group Databasebeta| order | 26100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊#15668504 |
| Fitting, derived, Hall | C9×C25×C29 ⋊ C4 |
| Hall | C25×C29 ⋊ Dic9 |
| Hall | C9×C29 ⋊ #1035 |
| Hall | C9×C25 ⋊ Dic29 |
| Sylow | C29 ⋊ C9⋊#1035 |
| Sylow | C25 ⋊ Dic261 |
| Sylow | C9 ⋊ #15668504 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C25×C29 | C4 |
| Frattini | C3×C5 | C3⋊#10596816 |
| socle | C3×C5×C29 | ΓL(1,𝔽16) |
| prime radical | C3×C29×D25 | D3 |
| cosocle | C9×C29×D25 | C2 |
| LCS | G ▷ C9×C25×C29 | |
| UCS | C1 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6525 |
Polycyclic presentation:
2^2,3,5,29,3,5|a^2=b,c^3=f^2,d^5=g,c^a=c^2f,d^a=d^2g,e^a=e^28,f^a=f^2,g^a=g^2,d^b=d^4g^4,g^b=g^41830 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26100, 20);