Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C89×C128 ⋊ C2 |
| Sylow | C89 ⋊ M256 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C64 | C2×D89 |
| commutator, socle | C2×C89 | C2×C64 |
| Fitting | C89×C128 | C2 |
| prime radical | C2×D89 | C64 |
| cosocle | C64×C89 | C22 |
| hypercenter | C128 | D89 |
| hypocenter | C89 | M256 |
| LCS | G ▷ C2×C89 ▷ C89 | |
| UCS | C1 ◁ C64 ◁ C128 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11392 |
Polycyclic presentation:
2^8,89|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,g^2=h,b^a=bh,i^b=i^885792 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 57478);