Finite Group DatabasebetaFinite Group Databasebeta| order | 22072 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C23×C3×C5×C8×C11 (order 10560) · Inn(G) = C1 · Out(G) = C23×C3×C5×C8×C11 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C22072 |
| abelian | C8×C31×C89 |
| multiplicative | (ℤ/22073)ˣ, (ℤ/44146)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C2×C31×C89 |
| socle, prime radical | C2×C31×C89 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
16 conjugacy classes of subgroups.
22072 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | Dic11036, D22072 |
| maximal subgroup of | Dic11036, D22072 |
| maximal normal subgroup of | Dic11036, D22072 |
| automorphism group of | C22073 |
| outer automorphism group of | C22073 |
Past the SmallGroups library coverage — no SmallGroups id.