Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D3×#10597243 |
| unambiguous semidirect product | C3⋊(C22×C3×#10597243) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C3×#10597243) |
| Fitting, socle | C2×C32×C112 ⋊ C2×C5 |
| derived | C3×C112 ⋊ C22×C3×C5 |
| Hall | C32×#10597243 ⋊ C22 |
| Hall | C2×C3×D3×C112 ⋊ C5 |
| Hall | C32×C112 ⋊ C22×C5 |
| Sylow | C112 ⋊ C2×C3×C5×D3 |
| Sylow | C32 ⋊ C22×#10597243 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D3×#10597243 |
| commutator, cosocle, hypocenter | C3×C112 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C112 | C2×C5 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 ◁ C2×C3 | |
616 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 210 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
522 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 584);