Finite Group DatabasebetaFinite Group Databasebeta| order | 24720 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 16450560 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C24×C3×C5×C103 |
| multiplicative | (ℤ/54472)ˣ, (ℤ/57736)ˣ, (ℤ/74232)ˣ, (ℤ/81708)ˣ, (ℤ/86604)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
536 conjugacy classes of subgroups.
24720 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.