Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C3×C11 |
| direct product | #157×#10597245 |
| Fitting, socle, derived, Hall | C32×C112 ⋊ C4×C5 |
| Hall | C32×#10597245 ⋊ C4 |
| Hall | C112×#157 ⋊ C5 |
| Sylow | C112 ⋊ C5×#157 |
| Sylow | C32 ⋊ C4×#10597245 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C112 | C4×C5 |
| prime radical | C3⋊D3×#10597245 | C2 |
| cosocle | C112×C3⋊D3 | C2×C5 |
| LCS | G ▷ C32×C112 | |
| UCS | C1 | |
100 conjugacy classes of subgroups.
174 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 424);