Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| isoclinism | isoclinic class of C3⋊ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C112 · Schur multiplier (H2) = C3×C11 |
| direct product | C112×C3⋊ΓL(1,𝔽16) |
| unambiguous semidirect product | C3⋊(C112×ΓL(1,𝔽16)) |
| Fitting, socle, Hall | C32×C5×C112 ⋊ C4 |
| derived, Hall | C32×C5 ⋊ C4×C112 |
| Hall | C32×C112 ⋊ AGL(1,𝔽5) |
| Hall | C5×C112 ⋊ C3⋊Dic3 |
| Sylow | C32 ⋊ C112×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C112×C3⋊Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C112 | C3⋊ΓL(1,𝔽16) |
| commutator, hypocenter | C32×C5 | C4×C112 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C112 | C4 |
| prime radical | C32×D5×C112 | C2 |
| cosocle | C32×D5 | C2×C112 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C112 | |
504 conjugacy classes of subgroups.
2541 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 702);