Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C9⋊#14559102 |
| Fitting, derived, Hall | C5×C9×C112 ⋊ C4 |
| Hall | C9×C112 ⋊ Dic5 |
| Hall | C5×C112 ⋊ Dic9 |
| Sylow | C112 ⋊ Dic45 |
| Hall | C5×C9 ⋊ #92150 |
| Sylow | C9 ⋊ #14559102 |
| Sylow | C5 ⋊ C9⋊#92150 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C9×C112 | C4 |
| Frattini | C3 | C3⋊#14559102 |
| socle | C3×C5×C112 | Dic3 |
| prime radical | C3×C5×C11⋊D11 | D3 |
| cosocle | C5×C9×C11⋊D11 | C2 |
| LCS | G ▷ C5×C9×C112 | |
| UCS | C1 | |
108 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,11^2,3|a^2=b,c^3=g^2,c^a=c^2g,d^a=d^4,e^a=e^8f^7,f^a=e^8f^3,g^a=g^2,e^b=e^10,f^b=f^101398 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 287);