Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C2×C3 |
| Fitting, socle | C22×C3×C112 ⋊ C3×C5 |
| derived, Hall | C22×C112 ⋊ C32×C5 |
| Hall | C3×C112×A4 ⋊ C5 |
| Hall | C22×#10597244 ⋊ C32 |
| Sylow | C112 ⋊ C3×C5×A4 |
| Sylow | C22 ⋊ C32×#10597244 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | A4×#10597244 |
| commutator, cosocle, hypocenter | C22×C112 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C112 | C3×C5 |
| LCS | G ▷ C22×C112 | |
| UCS | C1 ◁ C3 | |
140 conjugacy classes of subgroups.
348 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 524);