Finite Group DatabasebetaFinite Group Databasebeta| order | 22112 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C691⋊#95 |
| Sylow | C691 ⋊ #95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×D691 |
| commutator | C2×C691 | C42 |
| Fitting | C22×C4×C691 | C2 |
| socle, prime radical, cosocle | C23×C691 | C22 |
| hypercenter | C22×C4 | D691 |
| hypocenter | C691 | #95 |
| LCS | G ▷ C2×C691 ▷ C691 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22112 |
Polycyclic presentation:
2^5,691|a^2=d,b^2=e,b^a=bc,f^b=f^6905540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22112, 53);