Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C5⋊#10624391 |
| unambiguous semidirect product | (C2×C5)⋊(C3×#10624391) |
| Fitting, socle | C2×C3×C5×C112 ⋊ D3 |
| derived | C5×C112⋊C3 ⋊ C22×C3 |
| Hall | C3×C5×C112⋊C3 ⋊ C22 |
| Hall | C3×C112⋊C3 ⋊ C2×D5 |
| Hall | C5×C112 ⋊ C2×C3×D3 |
| Sylow | C112 ⋊ C2×C3×D15 |
| Sylow | C5 ⋊ C2×C3×#10624391 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C5⋊#10624391 |
| commutator, cosocle, hypocenter | C5×C112⋊C3 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C112 | D3 |
| LCS | G ▷ C5×C112⋊C3 | |
| UCS | C1 ◁ C2×C3 | |
136 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
744 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 612);