Finite Group DatabasebetaFinite Group Databasebeta| order | 22320 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 552960 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C3×C4 |
| abelian | C32×C42×C5×C31 |
| multiplicative | (ℤ/22753)ˣ, (ℤ/24193)ˣ, (ℤ/45506)ˣ, (ℤ/48386)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C22×C32×C5×C31 |
| socle, prime radical | C22×C32×C5×C31 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
360 conjugacy classes of subgroups.
22320 conjugacy classes. The character table is too large to display.
| automorphism group of | C61×C373, C13×C1861 |
| outer automorphism group of | C61×C373, C13×C1861 |
Past the SmallGroups library coverage — no SmallGroups id.