Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3 |
| direct product | C32×#92150⋊C5 |
| unambiguous semidirect product | (C32×#92150)⋊C5 |
| Fitting, socle, Hall | C32×C112 ⋊ C4×C5 |
| derived, Sylow | C112 ⋊ C32×C4×C5 |
| Hall | C32×#10597243 ⋊ C4 |
| Hall | C32×#92150 ⋊ C5 |
| Hall | #10597243 ⋊ C32×C4 |
| Hall | #92150 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #92150⋊C5 |
| commutator, hypocenter | C112 | C32×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C112 | C4×C5 |
| prime radical | C32×#11925892 | C2 |
| cosocle | C11⋊D11 | C2×C32×C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C32 | |
216 conjugacy classes of subgroups.
234 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 428);