Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×#529×C89 ⋊ C2 |
| Sylow | C89 ⋊ #34829 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C23×D89 |
| commutator, socle, cosocle | C23×C89 | C25 |
| Frattini | C23 | C24×D89 |
| Fitting | C2×#529×C89 | C2 |
| hypercenter | C2×#529 | D89 |
| hypocenter | C89 | #34829 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#529 | |
2804 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5696 |
Polycyclic presentation:
2^8,89|c^2=gh,e^2=f,b^a=bf,c^a=cg,i^a=i^88,c^b=ch,d^b=dh,i^c=i^882540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 339756);