Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C27 |
| direct product | #95×Dic178 |
| Sylow | C89 ⋊ Q8×#95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D89 |
| commutator | C22×C89 | C22×C42 |
| Fitting | C4×#95×C89 | C2 |
| socle, prime radical, cosocle | C24×C89 | C24 |
| hypercenter | C4×#95 | D89 |
| hypocenter | C89 | Q8×#95 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C24 ◁ C4×#95 | |
2434 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22784 |
3620 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 91053);