Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3×C11 |
| unambiguous semidirect product | C3⋊(C3⋊#14559097) |
| Fitting, socle, derived, Hall | C32×C5×C112 ⋊ C4 |
| Hall | C32×C112 ⋊ AGL(1,𝔽5) |
| Hall | C5×C112 ⋊ C3⋊Dic3 |
| Sylow | C112 ⋊ C3⋊ΓL(1,𝔽16) |
| Hall | C32×C5 ⋊ #92150 |
| Sylow | C32 ⋊ #14559097 |
| Sylow | C5 ⋊ C3⋊(C3⋊#92150) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5×C112 | C4 |
| prime radical, cosocle | C32×C5⋊(C11⋊D11) | C2 |
| LCS | G ▷ C32×C5×C112 | |
| UCS | C1 | |
216 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,5,11^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^2,f^a=f^8g^7,g^a=f^8g^3,e^b=e^4,f^b=f^10,g^b=g^101371 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 701);