Finite Group DatabasebetaFinite Group Databasebeta| order | 22320 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1105920 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C32×C4×C5×C31 |
| multiplicative | (ℤ/28301)ˣ, (ℤ/28721)ˣ, (ℤ/33635)ˣ, (ℤ/34689)ˣ, (ℤ/36387)ˣ, (ℤ/36927)ˣ, (ℤ/37479)ˣ, (ℤ/39081)ˣ, (ℤ/43245)ˣ, (ℤ/46252)ˣ, (ℤ/49972)ˣ, (ℤ/52108)ˣ, (ℤ/56602)ˣ, (ℤ/57442)ˣ, (ℤ/66996)ˣ, (ℤ/67270)ˣ, (ℤ/69378)ˣ, (ℤ/72774)ˣ, (ℤ/73854)ˣ, (ℤ/74958)ˣ, (ℤ/78162)ˣ, (ℤ/86490)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C32×C5×C31 |
| socle, prime radical | C23×C32×C5×C31 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
648 conjugacy classes of subgroups.
22320 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.