Finite Group DatabasebetaFinite Group Databasebeta| order | 25200 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 116121600 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C24×C32×C7×C25 |
| multiplicative | (ℤ/51944)ˣ, (ℤ/58856)ˣ, (ℤ/59192)ˣ, (ℤ/75672)ˣ, (ℤ/77916)ˣ, (ℤ/88284)ˣ, (ℤ/88788)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C5 | C24×C32×C5×C7 |
| socle, prime radical | C24×C32×C5×C7 | C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2412 conjugacy classes of subgroups.
25200 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.