Finite Group DatabasebetaFinite Group Databasebeta| order | 22112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C691 ⋊ C2 |
| Sylow | C691 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D691 |
| commutator, socle | C2×C691 | C22×C4 |
| Fitting | M16×C691 | C2 |
| prime radical | #26010866 | C2 |
| cosocle | C4×C691 | C23 |
| hypercenter | M16 | D691 |
| hypocenter | C691 | #131 |
| LCS | G ▷ C2×C691 ▷ C691 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11056 |
Polycyclic presentation:
2^5,691|a^2=d,d^2=e,f^a=f^690,c^b=ce,f^c=f^6903470 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22112, 154);