Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | (C11⋊(C11⋊AGL(1,𝔽5)))⋊C9 |
| derived, Hall | C5×C112 ⋊ C4×C9 |
| Hall | C5×C112⋊C9 ⋊ C4 |
| Hall | C11⋊(C11⋊AGL(1,𝔽5)) ⋊ C9 |
| Hall | C112⋊C9 ⋊ AGL(1,𝔽5) |
| Sylow | C112 ⋊ C9×AGL(1,𝔽5) |
| Sylow | C5 ⋊ (C11⋊Dic11)⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C11⋊(C11⋊AGL(1,𝔽5)))⋊C3 |
| commutator, hypocenter | C5×C112 | C4×C9 |
| Fitting, socle | C3×C5×C112 | C3×C4 |
| prime radical, cosocle | C3×D5×C112 | C2×C3 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 ◁ C3 | |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,5,11^2,3|a^2=c,b^3=g,d^a=d^2,e^a=e^10,f^a=f^10,e^b=e^7f^5,f^b=e^4f^3,d^c=d^4285 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 220);