Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C11 |
| direct product | ΓL(1,𝔽16)×C112⋊C3 |
| unambiguous semidirect product | C3⋊(AGL(1,𝔽5)×C112⋊C3) |
| unambiguous semidirect product | (C112×ΓL(1,𝔽16))⋊C3 |
| Fitting, socle, derived | C3×C5×C112 ⋊ C3×C4 |
| Hall | C3×C5×C112⋊C3 ⋊ C4 |
| Hall | C3×C112⋊C3 ⋊ AGL(1,𝔽5) |
| Hall | C5×C112 ⋊ C3×Dic3 |
| Sylow | C112 ⋊ C3×ΓL(1,𝔽16) |
| Sylow | C5 ⋊ Dic3×C112⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C112 | C3×C4 |
| prime radical | C3×D5×C112⋊C3 | C2 |
| cosocle | C3×D5×C112 | C2×C3 |
| LCS | G ▷ C3×C5×C112 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
387 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 549);