Finite Group DatabasebetaFinite Group Databasebeta| order | 24840 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 76032 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C3×C4×C5×C9×C23 |
| multiplicative | (ℤ/25159)ˣ, (ℤ/25567)ˣ, (ℤ/25699)ˣ, (ℤ/26239)ˣ, (ℤ/37287)ˣ, (ℤ/50318)ˣ, (ℤ/51134)ˣ, (ℤ/51398)ˣ, (ℤ/52478)ˣ, (ℤ/74574)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C22×C32×C5×C23 |
| socle, prime radical | C22×C32×C5×C23 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
320 conjugacy classes of subgroups.
24840 conjugacy classes. The character table is too large to display.
| automorphism group of | C139×C181, C37×C691, C31×C829, … |
| outer automorphism group of | C139×C181, C37×C691, C31×C829, … |
Past the SmallGroups library coverage — no SmallGroups id.