Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C3 |
| direct product | C3⋊Dic3×#10597244 |
| unambiguous semidirect product | C3⋊(Dic3×#10597244) |
| derived, Hall | C32×C112 ⋊ C4×C5 |
| Hall | C32×#10597244 ⋊ C4 |
| Hall | C112×C3⋊Dic3 ⋊ C5 |
| Sylow | C112 ⋊ C5×C3⋊Dic3 |
| Sylow | C32 ⋊ C4×#10597244 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊D3×#10597244 |
| commutator, hypocenter | C32×C112 | C4×C5 |
| Fitting, socle, cosocle | C2×C32×C112 | C2×C5 |
| prime radical | C2×C32×#10597244 | C2 |
| LCS | G ▷ C32×C112 | |
| UCS | C1 ◁ C2 | |
180 conjugacy classes of subgroups.
348 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 357);