Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C112 · Schur multiplier (H2) = C3×C11 |
| direct product | C32×C112×AGL(1,𝔽5) |
| Fitting, socle, Hall | C32×C5×C112 ⋊ C4 |
| derived, Sylow | C5 ⋊ C32×C4×C112 |
| Hall | C5×C112 ⋊ C32×C4 |
| Hall | C32×C5 ⋊ C4×C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C112 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C32×C4×C112 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C112 | C4 |
| prime radical | C32×D5×C112 | C2 |
| cosocle | D5 | C2×C32×C112 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C32×C112 | |
504 conjugacy classes of subgroups.
5445 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 640);