Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C9⋊#11925896 |
| unambiguous semidirect product | (C2×C9)⋊#11925896 |
| Fitting | C2×C9×C112 ⋊ C2×C5 |
| derived, Hall | C9×C112 ⋊ C22×C5 |
| Hall | C9×#10597245 ⋊ C22 |
| Hall | C2×C11×D99 ⋊ C5 |
| Hall | #10597245 ⋊ C2×D9 |
| Sylow | C112 ⋊ C2×C5×D9 |
| Sylow | C9 ⋊ C2×#11925896 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C9⋊#11925896 |
| commutator, cosocle, hypocenter | C9×C112 | C22×C5 |
| Frattini | C3 | C2×C3⋊#11925896 |
| Fitting | C2×C9×C112 | C2×C5 |
| socle | C2×C3×C112 | C5×D3 |
| LCS | G ▷ C9×C112 | |
| UCS | C1 ◁ C2 | |
126 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
282 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 245);