Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3×C11 |
| direct product | C3×#14559102⋊C3 |
| unambiguous semidirect product | #14559102⋊C32 |
| unambiguous semidirect product | (C3×#14559102)⋊C3 |
| Fitting, socle | C3×C5×C112 ⋊ C3×C4 |
| derived, Hall | C5×C112 ⋊ C32×C4 |
| Hall | C3×C5×C112⋊C3 ⋊ C4 |
| Hall | #14559102 ⋊ C32 |
| Hall | C3×C112⋊C3 ⋊ Dic5 |
| Sylow | C112 ⋊ C32×Dic5 |
| Sylow | C5 ⋊ C3×#92150⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #14559102⋊C3 |
| commutator, hypocenter | C5×C112 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C112 | C3×C4 |
| prime radical | C3×C5×(C11⋊D11)⋊C3 | C2 |
| cosocle | C5×C11⋊D11 | C2×C32 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 ◁ C3 | |
88 conjugacy classes of subgroups.
222 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 540);