Finite Group DatabasebetaFinite Group Databasebeta| order | 22112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×D4×C691 ⋊ C2 |
| Sylow | C691 ⋊ #127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D691 |
| commutator, socle, cosocle | C22×C691 | C23 |
| Fitting | C2×D4×C691 | C2 |
| hypercenter | C2×D4 | D691 |
| hypocenter | C691 | #127 |
| LCS | G ▷ C22×C691 ▷ C691 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11056 |
Polycyclic presentation:
2^5,691|b^2=d,c^2=e,b^a=bd,c^a=ce,f^c=f^6903464 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22112, 142);