Finite Group DatabasebetaFinite Group Databasebeta| order | 26820 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊#15688382 |
| Fitting, derived, Hall | C5×C9×C149 ⋊ C4 |
| Hall | C9×C149 ⋊ AGL(1,𝔽5) |
| Hall | C5×C149 ⋊ Dic9 |
| Sylow | C149 ⋊ C9⋊AGL(1,𝔽5) |
| Hall | C5×C9 ⋊ #10597010 |
| Sylow | C9 ⋊ #15688382 |
| Sylow | C5 ⋊ C9⋊#10597010 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C9×C149 | C4 |
| Frattini | C3 | C3⋊#15688382 |
| socle | C3×C5×C149 | Dic3 |
| prime radical | C3×D745 | D3 |
| cosocle | C9×D745 | C2 |
| LCS | G ▷ C5×C9×C149 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6705 |
Polycyclic presentation:
2^2,3,5,149,3|a^2=b,c^3=f^2,c^a=c^2f,d^a=d^2,e^a=e^44,f^a=f^2,d^b=d^4,e^b=e^1481686 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26820, 21);