Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C22×C32×#10597244 |
| Fitting, socle, Hall | C22×C32×C112 ⋊ C5 |
| derived, Sylow | C112 ⋊ C22×C32×C5 |
| Hall | C32×C112 ⋊ C22×C5 |
| Hall | C22×C112 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C32 | #10597244 |
| commutator, cosocle, hypocenter | C112 | C22×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C32×C112 | C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C22×C32 | |
300 conjugacy classes of subgroups.
1044 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 623);