Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C89 ⋊ #13950 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D89 |
| commutator | C23×C89 | C23×C4 |
| Fitting | C89×#1434 | C2 |
| socle, prime radical, cosocle | C24×C89 | C24 |
| hypercenter | #1434 | D89 |
| hypocenter | C89 | #13950 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C24 ◁ #1434 | |
1182 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22784 |
Polycyclic presentation:
2^8,89|a^2=h,b^2=ef,c^2=e,d^2=eg,b^a=be,c^a=cf,d^a=de,i^a=i^88,c^b=cg,i^b=i^88,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, 92216);