Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C89×#2419 ⋊ C2 |
| Sylow | C89 ⋊ #36763 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D89 |
| commutator, socle, cosocle | C23×C89 | C25 |
| Fitting | C89×#2419 | C2 |
| prime radical | C2×#15667984 | C22 |
| hypercenter | #2419 | D89 |
| hypocenter | C89 | #36763 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #2419 | |
1646 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11392 |
Polycyclic presentation:
2^8,89|b^2=g,c^2=fg,d^2=f,b^a=bf,c^a=cg,d^a=df,e^a=efh,c^b=ch,d^b=dfh,i^b=i^88,i^c=i^88,i^d=i^881724 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 377544);