Finite Group DatabasebetaFinite Group Databasebeta| order | 24600 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 6451200 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C5 |
| abelian | C23×C3×C52×C41 |
| multiplicative | (ℤ/28303)ˣ, (ℤ/40623)ˣ, (ℤ/54164)ˣ, (ℤ/56606)ˣ, (ℤ/81246)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
512 conjugacy classes of subgroups.
24600 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.