Finite Group DatabasebetaFinite Group Databasebeta| order | 18560 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 22020096 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C4×C5×C8×C29 |
| multiplicative | (ℤ/36285)ˣ, (ℤ/38445)ˣ, (ℤ/38704)ˣ, (ℤ/41008)ˣ, (ℤ/46600)ˣ, (ℤ/47200)ˣ, (ℤ/48380)ˣ, (ℤ/51260)ˣ, (ℤ/69900)ˣ, (ℤ/72570)ˣ, (ℤ/76890)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4 | C24×C5×C29 |
| socle, prime radical | C24×C5×C29 | C2×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1520 conjugacy classes of subgroups.
18560 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.