Finite Group DatabasebetaFinite Group Databasebeta| order | 26820 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D45⋊D149 |
| unambiguous semidirect product | D745⋊D9 |
| unambiguous semidirect product | D1341⋊D5 |
| Fitting, derived, Hall | C5×C9×C149 ⋊ C22 |
| Hall | C9×C149 ⋊ C2×D5 |
| Hall | C5×C149 ⋊ C2×D9 |
| Sylow | C149 ⋊ D5×D9 |
| Hall | C5×C9 ⋊ C2×D149 |
| Sylow | C9 ⋊ D5×D149 |
| Sylow | C5 ⋊ D9×D149 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C9×C149 | C22 |
| Frattini | C3 | D15⋊D149 |
| socle | C3×C5×C149 | C2×D3 |
| LCS | G ▷ C5×C9×C149 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6705 |
Polycyclic presentation:
2^2,3,5,149,3|c^3=f^2,d^a=d^4,e^a=e^148,c^b=c^2f,d^b=d^4,f^b=f^21800 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26820, 28);