Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C3⋊D3×D121⋊C5 |
| unambiguous semidirect product | D121⋊(C5×C3⋊D3) |
| unambiguous semidirect product | (C3×D121⋊C5)⋊D3 |
| unambiguous semidirect product | (C3⋊D3×D121)⋊C5 |
| Fitting, derived, Hall | C32×C121 ⋊ C22×C5 |
| Hall | C32×C121⋊C5 ⋊ C22 |
| Hall | C3⋊D3×D121 ⋊ C5 |
| Hall | C121⋊C5 ⋊ C2×C3⋊D3 |
| Sylow | C121 ⋊ C2×C5×C3⋊D3 |
| Sylow | C32 ⋊ C2×D121⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C121 | C22×C5 |
| Frattini | C11 | C3⋊D3×AGL(1,𝔽11) |
| socle | C32×C11 | C2×AGL(1,𝔽11) |
| LCS | G ▷ C32×C121 | |
| UCS | C1 | |
180 conjugacy classes of subgroups.
132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 61);