Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×#11925890 |
| Fitting, socle | C2×C32×C112 ⋊ D5 |
| derived, Hall | #10597245 ⋊ C22×C32 |
| Hall | C32×#10597245 ⋊ C22 |
| Hall | C32×C112 ⋊ C2×D5 |
| Sylow | C112 ⋊ C2×C32×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | #11925890 |
| commutator, cosocle, hypocenter | #10597245 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C112 | D5 |
| LCS | G ▷ #10597245 | |
| UCS | C1 ◁ C2×C32 | |
204 conjugacy classes of subgroups.
558 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 568);