Finite Group DatabasebetaFinite Group Databasebeta| order | 22112 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×C691⋊C8 |
| derived, Sylow | C691 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | D691 |
| commutator, hypocenter | C691 | C4×C8 |
| Frattini | C2×C4 | C2×D691 |
| Fitting | C42×C691 | C2 |
| socle, prime radical | C22×C691 | C2×C4 |
| cosocle | C2×C4×C691 | C22 |
| LCS | G ▷ C691 | |
| UCS | C1 ◁ C42 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22112 |
5552 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22112, 55);