Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C64 · Schur multiplier (H2) = C4 |
| direct product | C4×#19151317 |
| derived, Sylow | C89 ⋊ C4×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C32 | D89 |
| commutator, hypocenter | C89 | C4×C64 |
| Frattini | C2×C32 | C2×D89 |
| Fitting | C4×C32×C89 | C2 |
| socle, prime radical | C22×C89 | C2×C32 |
| cosocle | C2×C32×C89 | C22 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C4×C32 | |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22784 |
5888 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 57371);