Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C11 |
| direct product | AGL(1,𝔽5)×C112⋊C9 |
| unambiguous semidirect product | (C112×AGL(1,𝔽5))⋊C9 |
| derived, Hall | C5×C112 ⋊ C4×C9 |
| Hall | C5×C112⋊C9 ⋊ C4 |
| Hall | C112×AGL(1,𝔽5) ⋊ C9 |
| Sylow | C112 ⋊ C9×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×C112⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | AGL(1,𝔽5)×C112⋊C3 |
| commutator, hypocenter | C5×C112 | C4×C9 |
| Fitting, socle | C3×C5×C112 | C3×C4 |
| prime radical, cosocle | C3×D5×C112 | C2×C3 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 ◁ C3 | |
84 conjugacy classes of subgroups.
645 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 221);