Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#10624391⋊D3 |
| Fitting, socle | C3×C5×C112 ⋊ C2×D3 |
| derived, Hall | C3×C112⋊C3 ⋊ C22×C5 |
| Hall | C3×C5×C112⋊C3 ⋊ C22 |
| Hall | C5×C112 ⋊ D32 |
| Sylow | C112 ⋊ C5×D32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #10624391⋊D3 |
| commutator, cosocle, hypocenter | C3×C112⋊C3 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C112 | C2×D3 |
| LCS | G ▷ C3×C112⋊C3 | |
| UCS | C1 ◁ C5 | |
136 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
345 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 541);