Finite Group DatabasebetaFinite Group Databasebeta| order | 29328 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 211968 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C4×C13×C47 |
| multiplicative | (ℤ/42805)ˣ, (ℤ/44997)ˣ, (ℤ/47697)ˣ, (ℤ/55035)ˣ, (ℤ/58664)ˣ, (ℤ/59996)ˣ, (ℤ/63596)ˣ, (ℤ/85610)ˣ, (ℤ/87996)ˣ, (ℤ/89994)ˣ, (ℤ/95394)ˣ, (ℤ/110070)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C3×C13×C47 |
| socle, prime radical | C23×C3×C13×C47 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
216 conjugacy classes of subgroups.
29328 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.