Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3⋊(C3⋊((C11⋊C5)⋊D11)) |
| unambiguous semidirect product | (C2×C3)⋊(C3⋊((C11⋊C5)⋊D11)) |
| unambiguous semidirect product | (C2×C11⋊C5)⋊(C3⋊D33) |
| Fitting, socle | C2×C32×C112 ⋊ C2×C5 |
| derived, Hall | C32×C112 ⋊ C22×C5 |
| Hall | C32×C11×C11⋊C5 ⋊ C22 |
| Hall | C2×C3⋊(C3⋊(C11⋊D11)) ⋊ C5 |
| Hall | C11×C11⋊C5 ⋊ C2×C3⋊D3 |
| Sylow | C112 ⋊ C2×C5×C3⋊D3 |
| Sylow | C32 ⋊ C2×(C11⋊C5)⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(C3⋊((C11⋊C5)⋊D11)) |
| commutator, cosocle, hypocenter | C32×C112 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C112 | C2×C5 |
| LCS | G ▷ C32×C112 | |
| UCS | C1 ◁ C2 | |
300 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
708 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 597);