Finite Group DatabasebetaFinite Group Databasebeta| order | 22052 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C42×C9×C37 (order 10656) · Inn(G) = C1 · Out(G) = C2×C42×C9×C37 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C22052 |
| abelian | C4×C37×C149 |
| multiplicative | (ℤ/22201)ˣ, (ℤ/44402)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C2×C37×C149 |
| socle, prime radical | C2×C37×C149 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
12 conjugacy classes of subgroups.
22052 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | Dic11026, D22052 |
| maximal subgroup of | Dic11026, D22052 |
| maximal normal subgroup of | Dic11026, D22052 |
| automorphism group of | C22201 |
| outer automorphism group of | C22201 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22052, 1);