Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Sylow | C89 ⋊ C4×#387 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D89 |
| commutator | C22×C89 | C22×C42 |
| Fitting | C89×#1436 | C2 |
| socle, prime radical, cosocle | C24×C89 | C24 |
| hypercenter | #1436 | D89 |
| hypocenter | C89 | C4×#387 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C24 ◁ #1436 | |
1742 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22784 |
Polycyclic presentation:
2^8,89|a^2=g,b^2=h,c^2=e,d^2=eg,b^a=be,c^a=cf,i^a=i^88,i^c=i^88,i^d=i^882576 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 90748);