Finite Group DatabasebetaFinite Group Databasebeta| order | 32472 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 403200 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C9×C11×C41 |
| multiplicative | (ℤ/36271)ˣ, (ℤ/49551)ˣ, (ℤ/50991)ˣ, (ℤ/51543)ˣ, (ℤ/66068)ˣ, (ℤ/67988)ˣ, (ℤ/72542)ˣ, (ℤ/99102)ˣ, (ℤ/101982)ˣ, (ℤ/103086)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C23×C3×C11×C41 |
| socle, prime radical | C23×C3×C11×C41 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
192 conjugacy classes of subgroups.
32472 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.