Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | ((C11⋊D11)⋊C9)⋊D5 |
| derived, Hall | C5×C112⋊C9 ⋊ C22 |
| Hall | C112⋊C9 ⋊ C2×D5 |
| Hall | C5×C112 ⋊ C2×D9 |
| Sylow | C112 ⋊ C2×D45 |
| Sylow | C5 ⋊ #14546095⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×C112⋊C9 | C22 |
| Frattini | C3 | ((C11⋊D11)⋊C3)⋊D5 |
| Fitting, socle | C3×C5×C112 | C2×D3 |
| LCS | G ▷ C5×C112⋊C9 | |
| UCS | C1 | |
108 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,11^2,3|c^3=g^2,c^a=c^2g,d^a=d^4,e^a=e^3f^10,f^a=e^8f^8,g^a=g^2,e^b=e^10,f^b=f^10,e^c=e^2f^10,f^c=e^7f^8213 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 223);