Finite Group DatabasebetaFinite Group Databasebeta| order | 18504 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2064384 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C23×C32×C257 |
| multiplicative | (ℤ/32403)ˣ, (ℤ/43204)ˣ, (ℤ/55548)ˣ, (ℤ/64806)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
192 conjugacy classes of subgroups.
18504 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.