Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C11 |
| unambiguous semidirect product | (C3⋊D3)⋊(C5⋊(C11⋊D11)) |
| Fitting, socle, derived, Hall | C32×C5×C112 ⋊ C22 |
| Hall | C32×C112 ⋊ C2×D5 |
| Hall | C5×C112 ⋊ D32 |
| Sylow | C112 ⋊ (C3⋊D3)⋊D5 |
| Hall | C32×C5 ⋊ C2×C11⋊D11 |
| Sylow | C32 ⋊ C2×C5⋊(C11⋊D11) |
| Sylow | C5 ⋊ (C3⋊D3)⋊(C11⋊D11) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C5×C112 | C22 |
| LCS | G ▷ C32×C5×C112 | |
| UCS | C1 | |
616 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,5,11^2|d^a=d^2,e^a=e^4,f^a=f^10,g^a=g^10,c^b=c^2,d^b=d^21821 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 695);