Finite Group DatabasebetaFinite Group Databasebeta| order | 22112 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C691⋊C32 |
| derived, Sylow | C691 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | D691 |
| commutator, hypocenter | C691 | C32 |
| Fitting, cosocle | C16×C691 | C2 |
| socle, prime radical | C2×C691 | C16 |
| LCS | G ▷ C691 | |
| UCS | C1 ◁ C16 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22112 |
Polycyclic presentation:
2^5,691|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^6905552 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22112, 52);