Finite Group DatabasebetaFinite Group Databasebeta| order | 22112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#26010866 |
| Fitting | C22×C4×C691 ⋊ C2 |
| Sylow | C691 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D691 |
| commutator, cosocle | C2×C691 | C24 |
| Frattini | C2 | C23×D691 |
| Fitting | C22×C4×C691 | C2 |
| socle | C22×C691 | C23 |
| hypercenter | C22×C4 | D691 |
| hypocenter | C691 | C2×#41 |
| LCS | G ▷ C2×C691 ▷ C691 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11056 |
5540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22112, 189);