Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C89 ⋊ #34337 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D89 |
| commutator | C22×C89 | C24×C4 |
| Fitting | C42×Q8×C89 | C2 |
| socle, prime radical, cosocle | C23×C89 | C25 |
| hypercenter | C42×Q8 | D89 |
| hypocenter | C89 | #34337 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ C42×Q8 | |
2124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22784 |
Polycyclic presentation:
2^8,89|a^2=h,b^2=f,c^2=g,d^2=f,e^2=fgh,b^a=bf,c^a=cg,e^a=ef,i^a=i^88,d^b=df3608 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 332140);