Finite Group DatabasebetaFinite Group Databasebeta| order | 22112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C42×C691 ⋊ C2 |
| Sylow | C691 ⋊ #126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D691 |
| commutator, socle, cosocle | C22×C691 | C23 |
| Fitting | C42×C691 | C2 |
| prime radical | C22×D691 | C22 |
| hypercenter | C42 | D691 |
| hypocenter | C691 | #126 |
| LCS | G ▷ C22×C691 ▷ C691 | |
| UCS | C1 ◁ C22 ◁ C42 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11056 |
Polycyclic presentation:
2^5,691|b^2=de,c^2=d,b^a=bd,c^a=ce,f^a=f^6905534 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22112, 140);