Finite Group DatabasebetaFinite Group Databasebeta| order | 21776 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×#19129602 |
| unambiguous semidirect product | D1361⋊(C2×C4) |
| Fitting, socle | C22×C1361 ⋊ C4 |
| derived, Sylow | C1361 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #19129602 |
| commutator, hypocenter | C1361 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C1361 | C4 |
| prime radical | C22×D1361 | C2 |
| cosocle | D1361 | C23 |
| LCS | G ▷ C1361 | |
| UCS | C1 ◁ C22 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5444 |
1376 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21776, 51);