Finite Group DatabasebetaFinite Group Databasebeta| order | 22112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C16×C691 ⋊ C2 |
| Sylow | C691 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×D691 |
| commutator, socle | C2×C691 | C2×C8 |
| Fitting | C16×C691 | C2 |
| prime radical | C2×D691 | C8 |
| cosocle | C8×C691 | C22 |
| hypercenter | C16 | D691 |
| hypocenter | C691 | M32 |
| LCS | G ▷ C2×C691 ▷ C691 | |
| UCS | C1 ◁ C8 ◁ C16 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11056 |
Polycyclic presentation:
2^5,691|a^2=c,c^2=d,d^2=e,b^a=be,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, 85);