Finite Group DatabasebetaFinite Group Databasebeta| order | 22400 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 566231040 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4×C5 |
| abelian | C22×C4×C52×C7×C8 |
| multiplicative | (ℤ/39237)ˣ, (ℤ/43665)ˣ, (ℤ/46365)ˣ, (ℤ/46576)ˣ, (ℤ/49456)ˣ, (ℤ/52316)ˣ, (ℤ/56200)ˣ, (ℤ/56800)ˣ, (ℤ/58220)ˣ, (ℤ/61820)ˣ, (ℤ/78474)ˣ, (ℤ/84300)ˣ, (ℤ/87330)ˣ, (ℤ/92730)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4 | C24×C52×C7 |
| socle, prime radical | C24×C52×C7 | C2×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
6080 conjugacy classes of subgroups.
22400 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.